A069520 -id:A069520 - 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.

A232067 Numbers k such that sigma(k^2) and Sum_{d|k} d*sigma(d) are both multiples of k.

Original entry on oeis.org

1, 39, 793, 2379, 7137, 76921, 230763, 692289, 2076867, 8329831, 24989493, 53695813, 74968479, 161087439, 224905437, 243762649, 324863409, 375870691, 483262317, 731287947, 1127612073, 1449786951, 2094136707, 2193863841, 2631094837, 3382836219, 3606816823

Offset: 1

M. F. Hasler, Nov 24 2013

nonn

Intersection of A069520 and A232354.

Can these numbers be characterized as the terms of A232354 which do not have a factor in {11, 1093, ...}? Is this A090814, or (a subsequence of) A126197?

Donovan Johnson, Table of n, a(n) for n = 1..70

Cf. A000203, A069520, A232354.

fQ[n_] := Mod[DivisorSigma[1, n^2], n] == 0 && Mod[DivisorSum[n, #*DivisorSigma[1, #] &], n] == 0; Select[Range[100000], fQ] (* T. D. Noe, Nov 25 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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