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 Neighbors (Posted on 2014-04-18)
Find the smallest integer n such that both n-1 and n+1 have the same number of divisors as n.

 See The Solution Submitted by Ady TZIDON No Rating

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 re(2): computer solution | Comment 7 of 8 |
(In reply to re: computer solution by Jer)

Quints under 100,000:

low      high  # of divisors
11605 11609 8
12855 12859 8
13782 13786 8
19142 19146 8
21494 21498 8
28374 28378 8 |
28375 28379 8 | these make a hex
40311 40315 8
42805 42809 8
50582 50586 8
55254 55258 8
60231 60235 8
60663 60667 8
79094 79098 8
87655 87659 8
90181 90185 8 |
90182 90186 8 |  hex
95845 95849 8
99655 99659 8

and quads that are not in quints:

range    # of divisors
242 245 6
3655 3658 8
4503 4506 8
5943 5946 8
6853 6856 8
7256 7259 8
8392 8395 8
9367 9370 8
10983 10986 8
12565 12568 8
12872 12875 8
13255 13258 8
14312 14315 8
16133 16136 8
17095 17098 8
18469 18472 8
19045 19048 8
19940 19943 12
20165 20168 8
20965 20968 8
21368 21371 8
21512 21515 8
22855 22858 8
23989 23992 8
26885 26888 8
28135 28138 8
29605 29608 8
30583 30586 8
31735 31738 8
31910 31913 8
32005 32008 8
32792 32795 8
33062 33065 8
33608 33611 8
33845 33848 8
34069 34072 8
36392 36395 8
37256 37259 8
41335 41338 8
43304 43307 8
43526 43529 8
43766 43769 8
44213 44216 8
45686 45689 8
45733 45736 8
47845 47848 8
48054 48057 8
49147 49150 12
49765 49768 8
51752 51755 8
54103 54106 8
54585 54588 12
54966 54969 8
55063 55066 8
55976 55979 8
56343 56346 8
58952 58955 8
59815 59818 8
61142 61145 8
62343 62346 8
65334 65337 8
66952 66955 8
67015 67018 8
68104 68107 8
69303 69306 8
71095 71098 8
73927 73930 8
74053 74056 8
76262 76265 8
76982 76985 8
77432 77435 8
78535 78538 8
78872 78875 8
79591 79594 8
80726 80729 8
82855 82858 8
84469 84472 8
86887 86890 8
87896 87899 8
91495 91498 8
93063 93066 8
94262 94265 8
94645 94648 8
95384 95387 8
95414 95417 8
95512 95515 8
97255 97258 8
98102 98105 8
98984 98987 8

 Posted by Charlie on 2014-04-18 22:14:13

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