A232067 -id:A232067 - cp's OEIS frontend

A232354 Numbers k that divide sigma(k^2) where sigma is the sum of divisors function (A000203).

1, 39, 793, 2379, 7137, 13167, 76921, 78507, 230763, 238887, 549549, 692289, 863577, 1491633, 1672209, 2076867, 4317885, 7615179, 8329831, 10441431, 23402223, 24989493, 37776123, 53306253, 53695813, 55871145, 74968479, 83766969, 133854435, 144688401, 161087439, 189437391

Offset: 1

Alex Ratushnyak, Nov 22 2013

nonn

Squarefree terms are: 1, 39, 793, 2379, 76921, 230763, 8329831, 24989493, 53695813, 161087439, ... Quotients are: 1, 61, 873, 3783, 11737, 26543, 85563, 141911, 370773, 417263, 1155561, ... - Michel Marcus, Nov 23 2013

Many terms are also in sequence A069520, cf. A232067 for the intersection of these two sequences. - M. F. Hasler, Nov 24 2013

Donovan Johnson, Table of n, a(n) for n = 1..200
Jose Arnaldo Bebita Dris, A new approach to odd perfect numbers via GCDs, arXiv:2202.08116 [math.NT], 2022.

Cf. A000203, A007691, A065764, A069520, A227302, A232067, A232703, A232704.

Select[Range[10^5], Divisible[DivisorSigma[1, #^2], #] &] (* Alonso del Arte, Dec 06 2013 *)

isok(n) = (sigma(n^2) % n) == 0; \\ Michel Marcus, Nov 23 2013

A065764(a(n)) mod a(n) = 0.

A069520 Numbers k such that (1/k) * Sum_{d|k} d*sigma(d) is an integer.

Original entry on oeis.org

1, 39, 793, 1638, 2379, 2394, 7137, 8190, 11970, 14274, 18135, 19530, 30927, 31122, 35685, 36270, 50700, 61854, 71370, 76921, 81900, 92781, 99918, 119700, 154635, 155610, 185562, 195300, 230763, 253890, 269500, 299754, 304038, 309270

Offset: 1

Benoit Cloitre, Apr 16 2002

Sequence A232354 starts in a very similar way, and the two sequences have a common subsequence A232067 = (1, 39, 793, 2379, 7137, 76921, 230763, ...), but neither is a subsequence of the other. - M. F. Hasler, Nov 24 2013

Amiram Eldar, Table of n, a(n) for n = 1..500

Cf. A000203, A232067, A232354.

s[n_] := DivisorSum[n, # * DivisorSigma[1, #] &]; Select[Range[300000], Divisible[s[#], #] &] (* Amiram Eldar, May 14 2022 *)

is_A069520(n)=!(sumdiv(n,d,d*sigma(d))%n) \\ - M. F. Hasler, Nov 24 2013

cp's OEIS Frontend

A232354 Numbers k that divide sigma(k^2) where sigma is the sum of divisors function (A000203).

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