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prog.sf
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prog.sf
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#!/usr/bin/ruby
# Numbers k such that the sum of divisors of k (A000203) and the sum of proper divisors of k (A001065) are both triangular numbers (A000217).
# https://oeis.org/A329704
# Are 1 and 36 the only terms that are also triangular numbers?
# Assuming that such a term is also a perfect square, based on the data from A001110, if such a term exists, it must be greater than 10^353.
for k in (2..1e6) {
var t = polygonal(k, 3)
var a = t.inverse_sigma
for n in (a) {
if (n.sigma - n -> is_polygonal(3)) {
say n
}
}
}
__END__
#
## Some terms of A329704, computed using the inverse sigma function applied on triangular numbers.
#
1
2
5
36
54
473
441
6525
52577
124025
683820
1513754
1920552
6762923
6079931
14751657
17052782
17310942
49919939
36543714
60260967
372476909
562047389
251849052
364535720
783856979
1122603809
1084201689
670395564
670440852
2239241729
2284360733
824626800
2182908837
2487938201
2393957985
2306100332
4003025895
8210186009
11883589967
4678227684
5194927122
14538854609
26926218617
22614789545
12865159880
13167458360
24861819447
16688185878
36133539845
17807934000
39146468355
88597109453
42801425748
110315059217
70906440284
150437851247
70588308980
141827039637
220389070049
308251916039
210090511935