A232703 -id:A232703 - 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.

A232547 Numbers n such that sigma(n^2) mod sigma(n) = n.

Original entry on oeis.org

7581, 988893, 1658073, 468539757, 35124206517

Offset: 1

Alex Ratushnyak, Nov 25 2013

a(6) > 10^12. - Giovanni Resta, Jun 10 2016

Cf. A000203 (sigma(n) = sum of divisors of n), A065764, A232703, A247222.

a(5) from Giovanni Resta, Jun 10 2016

A232704 Numbers n such that sigma(n)+n divides sigma(n^2).

Original entry on oeis.org

84889, 376443, 1260615, 2703555, 4883751, 7551847, 8894695, 9387081, 10142181, 12600825, 39450985, 57924711, 72978693, 73534503, 166503105, 428777995, 563715879, 578643967, 583540893, 1181555907, 1598569785, 1779455211, 2917138191, 3078534559, 3318534361

Offset: 1

Alex Ratushnyak, Nov 28 2013

nonn

Cf. A000203 (sigma(n) = sum of divisors of n).

Cf. A232547, A232703.

for(n=1, 10^8, if(sigma(n^2)%(sigma(n)+n)==0, print1(n ", "))) \\ Donovan Johnson, Nov 30 2013

a(23)-a(25) from Donovan Johnson, Nov 30 2013

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

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A232547 Numbers n such that sigma(n^2) mod sigma(n) = n.

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A232704 Numbers n such that sigma(n)+n divides sigma(n^2).

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