A274566 Numbers k such that sigma(k) == 0 (mod k-10).

6, 9, 11, 12, 14, 22, 40, 42, 46, 154, 190, 2656, 6490, 44650, 318250, 1360810, 1503370, 1788490, 3214090, 103712410, 3915380170, 6077111050, 9796360330, 10828121356, 33086522327050, 35966517350410, 11577093570201610, 16726040141635450, 576460762503970816

Offset: 1

Author

Paolo P. Lava, Jul 06 2016

Keywords

• nonn

Examples

			sigma(11) mod (11 - 10) = 12 mod 1 = 0.
		

Crossrefs

Contains subsequence A223607.

Contains 2 * odd terms of A101223.

Cf. A045770, A067702, A088833, A181598, A274551, A274552, A274553, A274554, A274556, A274557, A274558, A274559, A274560, A274561, A274562, A274563, A274564, A274565.

Programs

Magma

[n: n in [1..2*10^6] | n ne 10 and SumOfDivisors(n) mod (n-10) eq 0 ]; // Vincenzo Librandi, Jul 06 2016

Mathematica

k = -10; Select[Range[1, 10^7], # + k != 0 && Mod[DivisorSigma[1, #], # + k] == 0 &] (* Vincenzo Librandi, Jul 06 2016 *)

PARI

isok(k) = (k!=10) && !(Mod(sigma(k), k-10)); \\ Michel Marcus, May 30 2025

Extensions

a(19)-a(24) from Giovanni Resta, Jul 06 2016

a(25)-a(26) from Jud McCranie, Dec 02 2019

Terms 6,9 inserted and a(27)-a(29) added by Max Alekseyev, May 30 2025