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 Odd-abundant numbers. (Posted on 2018-07-21)
Abundant numbers are numbers whose factors add up to a number larger than the original number (see also 12). The sequence starts 12, 18, 20, 24, 30, 36, 40, 42, 48... note that those abundant numbers are all even.
Therefore, you may think that there are all even, or perhaps wonder if there are any odd abundant numbers at all.
There are indeed odd abundant numbers; however the smallest isn't until 945 - with a sum of factors = 975.

List three more odd-abundant numbers.

 No Solution Yet Submitted by Ady TZIDON No Rating

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 ... and then some | Comment 1 of 2
Odd abundant numbers and their sums of factors:

945 975
1575 1649
2205 2241
2835 2973
3465 4023
4095 4641
4725 5195
5355 5877
5775 6129
5985 6495
6435 6669
6615 7065
6825 7063
7245 7731
7425 7455
7875 8349
8085 8331
8415 8433
8505 8967
8925 8931
9135 9585
9555 9597
9765 10203
10395 12645
11025 11946
11655 12057
12285 14595
12705 12831
12915 13293
13545 13911
14175 15833
14805 15147
15015 17241
15435 15765
16065 18495
16695 17001
17325 21363
17955 20445
18585 18855
19215 19473
19305 21015
19635 21837
19845 21537
20475 24661
21105 21327
21735 24345
21945 24135
22275 22737
22365 22563
22995 23181
23205 25179
23625 26295
24255 29097
24885 25035
25245 26595
25515 26949
25935 27825
26145 26271
26565 28731
26775 31257
27405 30195
28035 28125
28215 29385
28665 33579
28875 31029
29295 32145
29835 30645
29925 34555
30555 30597
31185 38511
31395 33117
31815 31833
32175 35529
32445 32451
33075 37605
33345 33855
33495 35625
33915 35205
34125 35763
34155 34965
34965 37995
35805 37923
36225 41151
36855 44457
37125 37755
37485 42543
38115 44877
38745 41895
39375 41849
39585 41055
40425 44391
40635 43845
41055 41889
41895 47025
42075 44973
42315 43701
42525 47747
42735 44817
43065 43335
44415 47745
44625 45231
45045 59787
45675 51045
45885 46275
46035 46125
46305 49695
47025 49695
47355 49413
47775 51177
48195 56349
48825 54343
49665 51711
49725 51831
49875 49965
50085 53595
50505 51639
50715 55989
51765 51915
51975 67065
53235 60957
53865 62295
54285 56307
55125 60471
55575 57265
55755 59445
55965 56931
56595 58605
56925 59139
57645 61395
57915 64053
58275 64237
58695 59577
58905 75879
59535 64953
61215 63201
61425 77455
62475 64749
63315 67245
63525 68411
63945 69435
64155 64869
64575 70833
65205 74187
65835 83925
66825 68583
66885 67515
67095 71145
67275 68133
67725 74131
68145 70095
68355 73917
68985 73095
69615 87633
69825 71535
70455 72393
70785 74451
70875 80133
71775 73305
72345 72807
72765 91395
74025 80727
74655 78945
75075 91581
75735 81081
76545 80895
76725 78027
77175 84025
77385 79287
77805 96915
78435 82845
78975 79001
79695 100017
80325 98235
80535 80745
81081 81543
81585 87363
81675 83245
82005 83883
82215 92025
83265 83391
83475 90621
83655 87633
84105 88695
84315 86181
84525 85107
84645 89595
85995 105525
86625 108063
87885 97971
88725 92811
88935 93009
89505 93447
89775 108625
90405 96327
91035 100533
91245 93075
91575 92193
91665 96495
92565 94167
92925 100515
93555 116109
94185 115479
94815 100809
95445 100395
95865 97671
96075 103813
96525 111795
97335 102345
98175 116097
99225 114582

DefDbl A-Z
Dim fct(20, 1), crlf\$, tot, dvsr, num, f

Text1.Text = ""
crlf = Chr(13) + Chr(10)
Form1.Visible = True

For num = 3 To 99999 Step 2
f = factor(num)
tot = 0: dvsr = 1
If tot > num Then
Text1.Text = Text1.Text & num & Str(tot) & crlf
End If
Next

Text1.Text = Text1.Text & crlf & " done"
End Sub

dvsrSave = dvsr
For i = 0 To fct(wh, 1)
DoEvents
If i > 0 Then dvsr = dvsr * fct(wh, 0)
If wh = f Then
If dvsr <> num Then tot = tot + dvsr
Else
If wh < f Then addOn wh + 1
End If
Next
dvsr = dvsrSave
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

 Posted by Charlie on 2018-07-21 14:23:19

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