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How about 138? (Posted on 2018-05-10) |
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Let us define a sequence S(N):
a1= N, a n= sum of all factors of a n-1,
excluding a n-1 itself. Most sequences either converge or begin to repeat.
S(12) → 12,16,15,9,4,3,1,1,1...
S(6) → 6,6,6,6,...
S(220) → 220,284,220,284,220,284,...
Try to evaluate S(50), S(80), S(99).
How about S(138)?
WILL IT CONVERGE TO 1,1,1,...?
Please comment!
computer solution
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| Comment 1 of 4
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Below is a list of all the sequences for n through 300 except for n=276, whose sequence includes numbers that exceed the capacity of visual basic (needed more than 15 digits).
Using the list to answer the questions:
S(50) = 50, 43, 1, 1, ... S(80) = 80, 106, 56, 64, 63, 41, 1, 1, ... S(99) = 99, 57, 23, 1, 1, ...
S(138) does in fact converge to 1,1,...:
138, 150, 222, 234, 312, 528, 960, 2088, 3762, 5598, 6570, 10746, 13254, 13830, 19434, 20886, 21606, 25098, 26742, 26754, 40446, 63234, 77406, 110754, 171486, 253458, 295740, 647748, 1077612, 1467588, 1956812, 2109796, 1889486, 953914, 668966, 353578, 176792, 254128, 308832, 502104, 753216, 1240176, 2422288, 2697920, 3727264, 3655076, 2760844, 2100740, 2310856, 2455544, 3212776, 3751064, 3282196, 2723020, 3035684, 2299240, 2988440, 5297320, 8325080, 11222920, 15359480, 19199440, 28875608, 25266172, 19406148, 26552604, 40541052, 54202884, 72270540, 147793668, 228408732, 348957876, 508132204, 404465636, 303708376, 290504024, 312058216, 294959384, 290622016, 286081174, 151737434, 75868720, 108199856, 101437396, 76247552, 76099654, 42387146, 21679318, 12752594, 7278382, 3660794, 1855066, 927536, 932464, 1013592, 1546008, 2425752, 5084088, 8436192, 13709064, 20563656, 33082104, 57142536, 99483384, 245978376, 487384824, 745600776, 1118401224, 1677601896, 2538372504, 4119772776, 8030724504, 14097017496, 21148436904, 40381357656, 60572036544, 100039354704, 179931895322, 94685963278, 51399021218, 28358080762, 18046051430, 17396081338, 8698040672, 8426226964, 6319670230, 5422685354, 3217383766, 1739126474, 996366646, 636221402, 318217798, 195756362, 101900794, 54202694, 49799866, 24930374, 17971642, 11130830, 8904682, 4913018, 3126502, 1574810, 1473382, 736694, 541162, 312470, 249994, 127286, 69898, 34952, 34708, 26038, 13994, 7000, 11720, 14740, 19532, 16588, 18692, 14026, 7016, 6154, 3674, 2374, 1190, 1402, 704, 820, 944, 916, 694, 350, 394, 200, 265, 59, 1, 1, ...
The prime numbers of course all immediately converge to 1,1,..., and the vast majority of the others do. I looked for more that converged, to, say 6,6,..., and found that 25 does so, as well as 95, 119 and 143, each of which do go through 25 on their way to 6,6.
28 also repeats immediately but at least within the limits of the list nothing else goes through 28. As to what happens to 276, that's anyone's guess; I think it gets bigger and bigger forever, based on some experiments using UBASIC, but making some guesses there as to whether certain numbers are prime. Also I don't know if anything goes through a cycle like that for 220 and 284.
1, 1, 1 2, 1, 1 3, 1, 1 4, 3, 1, 1 5, 1, 1 6, 6, 6 7, 1, 1 8, 7, 1, 1 9, 4, 3, 1, 1 10, 8, 7, 1, 1 11, 1, 1 12, 16, 15, 9, 4, 3, 1, 1 13, 1, 1 14, 10, 8, 7, 1, 1 15, 9, 4, 3, 1, 1 16, 15, 9, 4, 3, 1, 1 17, 1, 1 18, 21, 11, 1, 1 19, 1, 1 20, 22, 14, 10, 8, 7, 1, 1 21, 11, 1, 1 22, 14, 10, 8, 7, 1, 1 23, 1, 1 24, 36, 55, 17, 1, 1 25, 6, 6 26, 16, 15, 9, 4, 3, 1, 1 27, 13, 1, 1 28, 28, 28 29, 1, 1 30, 42, 54, 66, 78, 90, 144, 259, 45, 33, 15, 9, 4, 3, 1, 1 31, 1, 1 32, 31, 1, 1 33, 15, 9, 4, 3, 1, 1 34, 20, 22, 14, 10, 8, 7, 1, 1 35, 13, 1, 1 36, 55, 17, 1, 1 37, 1, 1 38, 22, 14, 10, 8, 7, 1, 1 39, 17, 1, 1 40, 50, 43, 1, 1 41, 1, 1 42, 54, 66, 78, 90, 144, 259, 45, 33, 15, 9, 4, 3, 1, 1 43, 1, 1 44, 40, 50, 43, 1, 1 45, 33, 15, 9, 4, 3, 1, 1 46, 26, 16, 15, 9, 4, 3, 1, 1 47, 1, 1 48, 76, 64, 63, 41, 1, 1 49, 8, 7, 1, 1 50, 43, 1, 1 51, 21, 11, 1, 1 52, 46, 26, 16, 15, 9, 4, 3, 1, 1 53, 1, 1 54, 66, 78, 90, 144, 259, 45, 33, 15, 9, 4, 3, 1, 1 55, 17, 1, 1 56, 64, 63, 41, 1, 1 57, 23, 1, 1 58, 32, 31, 1, 1 59, 1, 1 60, 108, 172, 136, 134, 70, 74, 40, 50, 43, 1, 1 61, 1, 1 62, 34, 20, 22, 14, 10, 8, 7, 1, 1 63, 41, 1, 1 64, 63, 41, 1, 1 65, 19, 1, 1 66, 78, 90, 144, 259, 45, 33, 15, 9, 4, 3, 1, 1 67, 1, 1 68, 58, 32, 31, 1, 1 69, 27, 13, 1, 1 70, 74, 40, 50, 43, 1, 1 71, 1, 1 72, 123, 45, 33, 15, 9, 4, 3, 1, 1 73, 1, 1 74, 40, 50, 43, 1, 1 75, 49, 8, 7, 1, 1 76, 64, 63, 41, 1, 1 77, 19, 1, 1 78, 90, 144, 259, 45, 33, 15, 9, 4, 3, 1, 1 79, 1, 1 80, 106, 56, 64, 63, 41, 1, 1 81, 40, 50, 43, 1, 1 82, 44, 40, 50, 43, 1, 1 83, 1, 1 84, 140, 196, 203, 37, 1, 1 85, 23, 1, 1 86, 46, 26, 16, 15, 9, 4, 3, 1, 1 87, 33, 15, 9, 4, 3, 1, 1 88, 92, 76, 64, 63, 41, 1, 1 89, 1, 1 90, 144, 259, 45, 33, 15, 9, 4, 3, 1, 1 91, 21, 11, 1, 1 92, 76, 64, 63, 41, 1, 1 93, 35, 13, 1, 1 94, 50, 43, 1, 1 95, 25, 6, 6 96, 156, 236, 184, 176, 196, 203, 37, 1, 1 97, 1, 1 98, 73, 1, 1 99, 57, 23, 1, 1 100, 117, 65, 19, 1, 1 101, 1, 1 102, 114, 126, 186, 198, 270, 450, 759, 393, 135, 105, 87, 33, 15, 9, 4, 3, 1, 1 103, 1, 1 104, 106, 56, 64, 63, 41, 1, 1 105, 87, 33, 15, 9, 4, 3, 1, 1 106, 56, 64, 63, 41, 1, 1 107, 1, 1 108, 172, 136, 134, 70, 74, 40, 50, 43, 1, 1 109, 1, 1 110, 106, 56, 64, 63, 41, 1, 1 111, 41, 1, 1 112, 136, 134, 70, 74, 40, 50, 43, 1, 1 113, 1, 1 114, 126, 186, 198, 270, 450, 759, 393, 135, 105, 87, 33, 15, 9, 4, 3, 1, 1 115, 29, 1, 1 116, 94, 50, 43, 1, 1 117, 65, 19, 1, 1 118, 62, 34, 20, 22, 14, 10, 8, 7, 1, 1 119, 25, 6, 6 120, 240, 504, 1056, 1968, 3240, 7650, 14112, 32571, 27333, 12161, 1, 1 121, 12, 16, 15, 9, 4, 3, 1, 1 122, 64, 63, 41, 1, 1 123, 45, 33, 15, 9, 4, 3, 1, 1 124, 100, 117, 65, 19, 1, 1 125, 31, 1, 1 126, 186, 198, 270, 450, 759, 393, 135, 105, 87, 33, 15, 9, 4, 3, 1, 1 127, 1, 1 128, 127, 1, 1 129, 47, 1, 1 130, 122, 64, 63, 41, 1, 1 131, 1, 1 132, 204, 300, 568, 512, 511, 81, 40, 50, 43, 1, 1 133, 27, 13, 1, 1 134, 70, 74, 40, 50, 43, 1, 1 135, 105, 87, 33, 15, 9, 4, 3, 1, 1 136, 134, 70, 74, 40, 50, 43, 1, 1 137, 1, 1 138, 150, 222, 234, 312, 528, 960, 2088, 3762, 5598, 6570, 10746, 13254, 13830, 19434, 20886, 21606, 25098, 26742, 26754, 40446, 63234, 77406, 110754, 171486, 253458, 295740, 647748, 1077612, 1467588, 1956812, 2109796, 1889486, 953914, 668966, 353578, 176792, 254128, 308832, 502104, 753216, 1240176, 2422288, 2697920, 3727264, 3655076, 2760844, 2100740, 2310856, 2455544, 3212776, 3751064, 3282196, 2723020, 3035684, 2299240, 2988440, 5297320, 8325080, 11222920, 15359480, 19199440, 28875608, 25266172, 19406148, 26552604, 40541052, 54202884, 72270540, 147793668, 228408732, 348957876, 508132204, 404465636, 303708376, 290504024, 312058216, 294959384, 290622016, 286081174, 151737434, 75868720, 108199856, 101437396, 76247552, 76099654, 42387146, 21679318, 12752594, 7278382, 3660794, 1855066, 927536, 932464, 1013592, 1546008, 2425752, 5084088, 8436192, 13709064, 20563656, 33082104, 57142536, 99483384, 245978376, 487384824, 745600776, 1118401224, 1677601896, 2538372504, 4119772776, 8030724504, 14097017496, 21148436904, 40381357656, 60572036544, 100039354704, 179931895322, 94685963278, 51399021218, 28358080762, 18046051430, 17396081338, 8698040672, 8426226964, 6319670230, 5422685354, 3217383766, 1739126474, 996366646, 636221402, 318217798, 195756362, 101900794, 54202694, 49799866, 24930374, 17971642, 11130830, 8904682, 4913018, 3126502, 1574810, 1473382, 736694, 541162, 312470, 249994, 127286, 69898, 34952, 34708, 26038, 13994, 7000, 11720, 14740, 19532, 16588, 18692, 14026, 7016, 6154, 3674, 2374, 1190, 1402, 704, 820, 944, 916, 694, 350, 394, 200, 265, 59, 1, 1 139, 1, 1 140, 196, 203, 37, 1, 1 141, 51, 21, 11, 1, 1 142, 74, 40, 50, 43, 1, 1 143, 25, 6, 6 144, 259, 45, 33, 15, 9, 4, 3, 1, 1 145, 35, 13, 1, 1 146, 76, 64, 63, 41, 1, 1 147, 81, 40, 50, 43, 1, 1 148, 118, 62, 34, 20, 22, 14, 10, 8, 7, 1, 1 149, 1, 1 150, 222, 234, 312, 528, 960, 2088, 3762, 5598, 6570, 10746, 13254, 13830, 19434, 20886, 21606, 25098, 26742, 26754, 40446, 63234, 77406, 110754, 171486, 253458, 295740, 647748, 1077612, 1467588, 1956812, 2109796, 1889486, 953914, 668966, 353578, 176792, 254128, 308832, 502104, 753216, 1240176, 2422288, 2697920, 3727264, 3655076, 2760844, 2100740, 2310856, 2455544, 3212776, 3751064, 3282196, 2723020, 3035684, 2299240, 2988440, 5297320, 8325080, 11222920, 15359480, 19199440, 28875608, 25266172, 19406148, 26552604, 40541052, 54202884, 72270540, 147793668, 228408732, 348957876, 508132204, 404465636, 303708376, 290504024, 312058216, 294959384, 290622016, 286081174, 151737434, 75868720, 108199856, 101437396, 76247552, 76099654, 42387146, 21679318, 12752594, 7278382, 3660794, 1855066, 927536, 932464, 1013592, 1546008, 2425752, 5084088, 8436192, 13709064, 20563656, 33082104, 57142536, 99483384, 245978376, 487384824, 745600776, 1118401224, 1677601896, 2538372504, 4119772776, 8030724504, 14097017496, 21148436904, 40381357656, 60572036544, 100039354704, 179931895322, 94685963278, 51399021218, 28358080762, 18046051430, 17396081338, 8698040672, 8426226964, 6319670230, 5422685354, 3217383766, 1739126474, 996366646, 636221402, 318217798, 195756362, 101900794, 54202694, 49799866, 24930374, 17971642, 11130830, 8904682, 4913018, 3126502, 1574810, 1473382, 736694, 541162, 312470, 249994, 127286, 69898, 34952, 34708, 26038, 13994, 7000, 11720, 14740, 19532, 16588, 18692, 14026, 7016, 6154, 3674, 2374, 1190, 1402, 704, 820, 944, 916, 694, 350, 394, 200, 265, 59, 1, 1 151, 1, 1 152, 148, 118, 62, 34, 20, 22, 14, 10, 8, 7, 1, 1 153, 81, 40, 50, 43, 1, 1 154, 134, 70, 74, 40, 50, 43, 1, 1 155, 37, 1, 1 156, 236, 184, 176, 196, 203, 37, 1, 1 157, 1, 1 158, 82, 44, 40, 50, 43, 1, 1 159, 57, 23, 1, 1 160, 218, 112, 136, 134, 70, 74, 40, 50, 43, 1, 1 161, 31, 1, 1 162, 201, 71, 1, 1 163, 1, 1 164, 130, 122, 64, 63, 41, 1, 1 165, 123, 45, 33, 15, 9, 4, 3, 1, 1 166, 86, 46, 26, 16, 15, 9, 4, 3, 1, 1 167, 1, 1 168, 312, 528, 960, 2088, 3762, 5598, 6570, 10746, 13254, 13830, 19434, 20886, 21606, 25098, 26742, 26754, 40446, 63234, 77406, 110754, 171486, 253458, 295740, 647748, 1077612, 1467588, 1956812, 2109796, 1889486, 953914, 668966, 353578, 176792, 254128, 308832, 502104, 753216, 1240176, 2422288, 2697920, 3727264, 3655076, 2760844, 2100740, 2310856, 2455544, 3212776, 3751064, 3282196, 2723020, 3035684, 2299240, 2988440, 5297320, 8325080, 11222920, 15359480, 19199440, 28875608, 25266172, 19406148, 26552604, 40541052, 54202884, 72270540, 147793668, 228408732, 348957876, 508132204, 404465636, 303708376, 290504024, 312058216, 294959384, 290622016, 286081174, 151737434, 75868720, 108199856, 101437396, 76247552, 76099654, 42387146, 21679318, 12752594, 7278382, 3660794, 1855066, 927536, 932464, 1013592, 1546008, 2425752, 5084088, 8436192, 13709064, 20563656, 33082104, 57142536, 99483384, 245978376, 487384824, 745600776, 1118401224, 1677601896, 2538372504, 4119772776, 8030724504, 14097017496, 21148436904, 40381357656, 60572036544, 100039354704, 179931895322, 94685963278, 51399021218, 28358080762, 18046051430, 17396081338, 8698040672, 8426226964, 6319670230, 5422685354, 3217383766, 1739126474, 996366646, 636221402, 318217798, 195756362, 101900794, 54202694, 49799866, 24930374, 17971642, 11130830, 8904682, 4913018, 3126502, 1574810, 1473382, 736694, 541162, 312470, 249994, 127286, 69898, 34952, 34708, 26038, 13994, 7000, 11720, 14740, 19532, 16588, 18692, 14026, 7016, 6154, 3674, 2374, 1190, 1402, 704, 820, 944, 916, 694, 350, 394, 200, 265, 59, 1, 1 169, 14, 10, 8, 7, 1, 1 170, 154, 134, 70, 74, 40, 50, 43, 1, 1 171, 89, 1, 1 172, 136, 134, 70, 74, 40, 50, 43, 1, 1 173, 1, 1 174, 186, 198, 270, 450, 759, 393, 135, 105, 87, 33, 15, 9, 4, 3, 1, 1 175, 73, 1, 1 176, 196, 203, 37, 1, 1 177, 63, 41, 1, 1 178, 92, 76, 64, 63, 41, 1, 1 179, 1, 1 180, 366, 378, 582, 594, 846, 1026, 1374, 1386, 2358, 2790, 4698, 6192, 11540, 12736, 12664, 11096, 11104, 10820, 11944, 10466, 5236, 6860, 9940, 14252, 14308, 15218, 10894, 6746, 3376, 3196, 2852, 2524, 1900, 2440, 3140, 3496, 3704, 3256, 3584, 4600, 6560, 9316, 8072, 7078, 3542, 3370, 2714, 1606, 1058, 601, 1, 1 181, 1, 1 182, 154, 134, 70, 74, 40, 50, 43, 1, 1 183, 65, 19, 1, 1 184, 176, 196, 203, 37, 1, 1 185, 43, 1, 1 186, 198, 270, 450, 759, 393, 135, 105, 87, 33, 15, 9, 4, 3, 1, 1 187, 29, 1, 1 188, 148, 118, 62, 34, 20, 22, 14, 10, 8, 7, 1, 1 189, 131, 1, 1 190, 170, 154, 134, 70, 74, 40, 50, 43, 1, 1 191, 1, 1 192, 316, 244, 190, 170, 154, 134, 70, 74, 40, 50, 43, 1, 1 193, 1, 1 194, 100, 117, 65, 19, 1, 1 195, 141, 51, 21, 11, 1, 1 196, 203, 37, 1, 1 197, 1, 1 198, 270, 450, 759, 393, 135, 105, 87, 33, 15, 9, 4, 3, 1, 1 199, 1, 1 200, 265, 59, 1, 1 201, 71, 1, 1 202, 104, 106, 56, 64, 63, 41, 1, 1 203, 37, 1, 1 204, 300, 568, 512, 511, 81, 40, 50, 43, 1, 1 205, 47, 1, 1 206, 106, 56, 64, 63, 41, 1, 1 207, 105, 87, 33, 15, 9, 4, 3, 1, 1 208, 226, 116, 94, 50, 43, 1, 1 209, 31, 1, 1 210, 366, 378, 582, 594, 846, 1026, 1374, 1386, 2358, 2790, 4698, 6192, 11540, 12736, 12664, 11096, 11104, 10820, 11944, 10466, 5236, 6860, 9940, 14252, 14308, 15218, 10894, 6746, 3376, 3196, 2852, 2524, 1900, 2440, 3140, 3496, 3704, 3256, 3584, 4600, 6560, 9316, 8072, 7078, 3542, 3370, 2714, 1606, 1058, 601, 1, 1 211, 1, 1 212, 166, 86, 46, 26, 16, 15, 9, 4, 3, 1, 1 213, 75, 49, 8, 7, 1, 1 214, 110, 106, 56, 64, 63, 41, 1, 1 215, 49, 8, 7, 1, 1 216, 384, 636, 876, 1196, 1156, 993, 335, 73, 1, 1 217, 39, 17, 1, 1 218, 112, 136, 134, 70, 74, 40, 50, 43, 1, 1 219, 77, 19, 1, 1 220, 284, 220, 284 221, 31, 1, 1 222, 234, 312, 528, 960, 2088, 3762, 5598, 6570, 10746, 13254, 13830, 19434, 20886, 21606, 25098, 26742, 26754, 40446, 63234, 77406, 110754, 171486, 253458, 295740, 647748, 1077612, 1467588, 1956812, 2109796, 1889486, 953914, 668966, 353578, 176792, 254128, 308832, 502104, 753216, 1240176, 2422288, 2697920, 3727264, 3655076, 2760844, 2100740, 2310856, 2455544, 3212776, 3751064, 3282196, 2723020, 3035684, 2299240, 2988440, 5297320, 8325080, 11222920, 15359480, 19199440, 28875608, 25266172, 19406148, 26552604, 40541052, 54202884, 72270540, 147793668, 228408732, 348957876, 508132204, 404465636, 303708376, 290504024, 312058216, 294959384, 290622016, 286081174, 151737434, 75868720, 108199856, 101437396, 76247552, 76099654, 42387146, 21679318, 12752594, 7278382, 3660794, 1855066, 927536, 932464, 1013592, 1546008, 2425752, 5084088, 8436192, 13709064, 20563656, 33082104, 57142536, 99483384, 245978376, 487384824, 745600776, 1118401224, 1677601896, 2538372504, 4119772776, 8030724504, 14097017496, 21148436904, 40381357656, 60572036544, 100039354704, 179931895322, 94685963278, 51399021218, 28358080762, 18046051430, 17396081338, 8698040672, 8426226964, 6319670230, 5422685354, 3217383766, 1739126474, 996366646, 636221402, 318217798, 195756362, 101900794, 54202694, 49799866, 24930374, 17971642, 11130830, 8904682, 4913018, 3126502, 1574810, 1473382, 736694, 541162, 312470, 249994, 127286, 69898, 34952, 34708, 26038, 13994, 7000, 11720, 14740, 19532, 16588, 18692, 14026, 7016, 6154, 3674, 2374, 1190, 1402, 704, 820, 944, 916, 694, 350, 394, 200, 265, 59, 1, 1 223, 1, 1 224, 280, 440, 640, 890, 730, 602, 454, 230, 202, 104, 106, 56, 64, 63, 41, 1, 1 225, 178, 92, 76, 64, 63, 41, 1, 1 226, 116, 94, 50, 43, 1, 1 227, 1, 1 228, 332, 256, 255, 177, 63, 41, 1, 1 229, 1, 1 230, 202, 104, 106, 56, 64, 63, 41, 1, 1 231, 153, 81, 40, 50, 43, 1, 1 232, 218, 112, 136, 134, 70, 74, 40, 50, 43, 1, 1 233, 1, 1 234, 312, 528, 960, 2088, 3762, 5598, 6570, 10746, 13254, 13830, 19434, 20886, 21606, 25098, 26742, 26754, 40446, 63234, 77406, 110754, 171486, 253458, 295740, 647748, 1077612, 1467588, 1956812, 2109796, 1889486, 953914, 668966, 353578, 176792, 254128, 308832, 502104, 753216, 1240176, 2422288, 2697920, 3727264, 3655076, 2760844, 2100740, 2310856, 2455544, 3212776, 3751064, 3282196, 2723020, 3035684, 2299240, 2988440, 5297320, 8325080, 11222920, 15359480, 19199440, 28875608, 25266172, 19406148, 26552604, 40541052, 54202884, 72270540, 147793668, 228408732, 348957876, 508132204, 404465636, 303708376, 290504024, 312058216, 294959384, 290622016, 286081174, 151737434, 75868720, 108199856, 101437396, 76247552, 76099654, 42387146, 21679318, 12752594, 7278382, 3660794, 1855066, 927536, 932464, 1013592, 1546008, 2425752, 5084088, 8436192, 13709064, 20563656, 33082104, 57142536, 99483384, 245978376, 487384824, 745600776, 1118401224, 1677601896, 2538372504, 4119772776, 8030724504, 14097017496, 21148436904, 40381357656, 60572036544, 100039354704, 179931895322, 94685963278, 51399021218, 28358080762, 18046051430, 17396081338, 8698040672, 8426226964, 6319670230, 5422685354, 3217383766, 1739126474, 996366646, 636221402, 318217798, 195756362, 101900794, 54202694, 49799866, 24930374, 17971642, 11130830, 8904682, 4913018, 3126502, 1574810, 1473382, 736694, 541162, 312470, 249994, 127286, 69898, 34952, 34708, 26038, 13994, 7000, 11720, 14740, 19532, 16588, 18692, 14026, 7016, 6154, 3674, 2374, 1190, 1402, 704, 820, 944, 916, 694, 350, 394, 200, 265, 59, 1, 1 235, 53, 1, 1 236, 184, 176, 196, 203, 37, 1, 1 237, 83, 1, 1 238, 194, 100, 117, 65, 19, 1, 1 239, 1, 1 240, 504, 1056, 1968, 3240, 7650, 14112, 32571, 27333, 12161, 1, 1 241, 1, 1 242, 157, 1, 1 243, 121, 12, 16, 15, 9, 4, 3, 1, 1 244, 190, 170, 154, 134, 70, 74, 40, 50, 43, 1, 1 245, 97, 1, 1 246, 258, 270, 450, 759, 393, 135, 105, 87, 33, 15, 9, 4, 3, 1, 1 247, 33, 15, 9, 4, 3, 1, 1 248, 232, 218, 112, 136, 134, 70, 74, 40, 50, 43, 1, 1 249, 87, 33, 15, 9, 4, 3, 1, 1 250, 218, 112, 136, 134, 70, 74, 40, 50, 43, 1, 1 251, 1, 1 252, 476, 532, 588, 1008, 2216, 1954, 980, 1414, 1034, 694, 350, 394, 200, 265, 59, 1, 1 253, 35, 13, 1, 1 254, 130, 122, 64, 63, 41, 1, 1 255, 177, 63, 41, 1, 1 256, 255, 177, 63, 41, 1, 1 257, 1, 1 258, 270, 450, 759, 393, 135, 105, 87, 33, 15, 9, 4, 3, 1, 1 259, 45, 33, 15, 9, 4, 3, 1, 1 260, 328, 302, 154, 134, 70, 74, 40, 50, 43, 1, 1 261, 129, 47, 1, 1 262, 134, 70, 74, 40, 50, 43, 1, 1 263, 1, 1 264, 456, 744, 1176, 2244, 3804, 5100, 10524, 14060, 17860, 22460, 24748, 20612, 15466, 11894, 6946, 3998, 2002, 2030, 2290, 1850, 1684, 1270, 1034, 694, 350, 394, 200, 265, 59, 1, 1 265, 59, 1, 1 266, 214, 110, 106, 56, 64, 63, 41, 1, 1 267, 93, 35, 13, 1, 1 268, 208, 226, 116, 94, 50, 43, 1, 1 269, 1, 1 270, 450, 759, 393, 135, 105, 87, 33, 15, 9, 4, 3, 1, 1 271, 1, 1 272, 286, 218, 112, 136, 134, 70, 74, 40, 50, 43, 1, 1 273, 175, 73, 1, 1 274, 140, 196, 203, 37, 1, 1 275, 97, 1, 1 276, 396, 696, 1104, 1872, 3770, 3790, 3050, 2716, 2772, 5964, 10164, 19628, 19684, 22876, 26404, 30044, 33796, 38780, 54628, 54684, 111300, 263676, 465668, 465724, 465780, 1026060, 2325540, 5335260, 11738916, 23117724, 45956820, 121129260, 266485716, 558454764, 1092873236, 1470806764, 1471882804, 1642613196, 2737688884, 2740114636, 2791337780, 4946860492, 4946860548, 9344070652, 9344070708, 15573451404, 27078171764, 27284104204, 27410152084, 27410152140, 76787720100, 220578719452, 254903331620, 361672366300, 603062136740, 921203207260, 1381419996068, 1395444575644, 1395478688996, 1395546402460, 2069258468900, 3065057872156, 3277068463844, 3429776547484, 3597527970596, 4028517592540, 5641400009252, 5641400009308, 5641400009364, 9709348326636, 16331909651988, 31948891146732, 54770416120644, 100509779504316, 208751080955844, 388416032284476, 749365894850244,***** 277, 1, 1 278, 142, 74, 40, 50, 43, 1, 1 279, 137, 1, 1 280, 440, 640, 890, 730, 602, 454, 230, 202, 104, 106, 56, 64, 63, 41, 1, 1 281, 1, 1 282, 294, 390, 618, 630, 1242, 1638, 2730, 5334, 6954, 7926, 7938, 12753, 7267, 785, 163, 1, 1 283, 1, 1 284, 220, 284, 220 285, 195, 141, 51, 21, 11, 1, 1 286, 218, 112, 136, 134, 70, 74, 40, 50, 43, 1, 1 287, 49, 8, 7, 1, 1 288, 531, 249, 87, 33, 15, 9, 4, 3, 1, 1 289, 18, 21, 11, 1, 1 290, 250, 218, 112, 136, 134, 70, 74, 40, 50, 43, 1, 1 291, 101, 1, 1 292, 226, 116, 94, 50, 43, 1, 1 293, 1, 1 294, 390, 618, 630, 1242, 1638, 2730, 5334, 6954, 7926, 7938, 12753, 7267, 785, 163, 1, 1 295, 65, 19, 1, 1 296, 274, 140, 196, 203, 37, 1, 1 297, 183, 65, 19, 1, 1 298, 152, 148, 118, 62, 34, 20, 22, 14, 10, 8, 7, 1, 1 299, 37, 1, 1 300, 568, 512, 511, 81, 40, 50, 43, 1, 1
DefDbl A-Z Dim crlf$, fct(20, 1), f, tot, prod, n2
Private Sub Form_Load() Form1.Visible = True Text1.Text = "" crlf = Chr(13) + Chr(10) For n = 1 To 300 s$ = LTrim(Str(n)) + "," n2 = n Do If n2 = 1 Then tot = 1 Else f = factor(n2): tot = 0: prod = 1: rpt = 0 addOn 1 End If n2 = tot: sa$ = Str(n2) If InStr(s, sa + ",") > 0 Then rpt = 1 If Len(sa) > 16 Then s = s + "*****" rpt = 1 Else s = s + sa End If If rpt = 0 Then s = s + "," DoEvents Loop Until rpt Text1.Text = Text1.Text & s & crlf Next n Text1.Text = Text1.Text & crlf & " done" End Sub
Sub addOn(wh) For i = 0 To fct(wh, 1) DoEvents saveProd = prod prod = prod * fct(wh, 0) ^ i If wh = f Then If prod <> n2 Then tot = tot + prod End If Else addOn (wh + 1) End If prod = saveProd Next i End Sub
Function factor(num) diffCt = 0: good = 1 n = Abs(num): If n > 0 Then limit = Sqr(n) Else limit = 0 If limit <> Int(limit) Then limit = Int(limit + 1) dv = 2: GoSub DivideIt dv = 3: GoSub DivideIt dv = 5: GoSub DivideIt dv = 7 Do Until dv > limit GoSub DivideIt: dv = dv + 4 '11 GoSub DivideIt: dv = dv + 2 '13 GoSub DivideIt: dv = dv + 4 '17 GoSub DivideIt: dv = dv + 2 '19 GoSub DivideIt: dv = dv + 4 '23 GoSub DivideIt: dv = dv + 6 '29 GoSub DivideIt: dv = dv + 2 '31 GoSub DivideIt: dv = dv + 6 '37 If INKEY$ = Chr$(27) Then s$ = Chr$(27): Exit Function Loop If n > 1 Then diffCt = diffCt + 1: fct(diffCt, 0) = n: fct(diffCt, 1) = 1 factor = diffCt Exit Function
DivideIt: cnt = 0 Do q = Int(n / dv) If q * dv = n And n > 0 Then n = q: cnt = cnt + 1: If n > 0 Then limit = Sqr(n) Else limit = 0 If limit <> Int(limit) Then limit = Int(limit + 1) Else Exit Do End If Loop If cnt > 0 Then diffCt = diffCt + 1 fct(diffCt, 0) = dv fct(diffCt, 1) = cnt End If Return End Function
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Posted by Charlie
on 2018-05-10 14:28:13 |
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