A274564 Numbers k such that sigma(k) == 0 (mod k-9).

6, 7, 8, 10, 11, 15, 19, 24, 33, 105, 33705, 33624064, 2199041081344

Offset: 1

Author

Paolo P. Lava, Jul 06 2016

Keywords

• nonn
• more

Examples

			sigma(10) mod (10 - 9) = 18 mod 1 = 0.
		

Crossrefs

Contains subsequence A223608.

Cf. A045770, A067702, A088833, A181598, A274551, A274552, A274553, A274554, A274556, A274557, A274558, A274559, A274560, A274561, A274562, A274563, A274565, A274566.

Programs

Magma

[n: n in [10..2*10^6] | SumOfDivisors(n) mod (n-9) eq 0 ]; // Vincenzo Librandi, Jul 06 2016

Mathematica

k = -9; Select[Range[Abs@k+1, 10^6], Mod[DivisorSigma[1, #], # + k] == 0 &] (* Vincenzo Librandi, Jul 06 2016 *)

PARI

isok(k) = (k!=9) && (Mod(sigma(k), k-9) == 0); \\ Michel Marcus, May 30 2025

Extensions

a(12)-a(13) from Giovanni Resta, Jul 06 2016

Terms 6,7,8 inserted by Max Alekseyev, May 29 2025