A227303 Numbers k such that k divides sigma(3*k).

1, 2, 4, 28, 40, 78, 90, 224, 360, 496, 546, 2016, 2184, 8128, 10080, 10920, 11880, 66528, 145236, 174592, 714240, 726180, 1571328, 4333056, 6168960, 7856640, 12065760, 15177600, 33550336, 47663616, 69521760, 80196480, 91963648, 99993600, 156854880, 459818240, 492101632

Offset: 1

Author

Alex Ratushnyak, Jul 05 2013

Keywords

• nonn

Comments

If k belongs to the sequence, then sigma(3*k)/k is an integer, so sigma(3*k)/(3*k) is either an integer or a third of an integer, so 3*k is either multiperfect or belongs to A160320 or A160321. - Michel Marcus, Jul 09 2013

Links

• Jud McCranie, Table of n, a(n) for n = 1..65

Crossrefs

Cf. A000203, A007691, A227302.

Cf. A160320, A160321.

Programs

Mathematica

k = 0; lst = {}; While[k < 10^11, If[ Mod[ DivisorSigma[1, 3 k], k] == 0, AppendTo[lst, k]]; k++]; lst (* Robert G. Wilson v, Mar 07 2021 *)

PARI

isok(k) = !(sigma(3*k) % k); \\ Michel Marcus, Mar 07 2021