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

6, 7, 8, 10, 11, 15, 19, 24, 33, 105, 33705, 33624064, 2199041081344, 36893488220433547264

Offset

1,1

Links

Table of n, a(n) for n=1..14.

Example

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

Mathematica

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

Prog

(Magma) [n: n in [10..2*10^6] | SumOfDivisors(n) mod (n-9) eq 0 ]; // Vincenzo Librandi, Jul 06 2016
(PARI) isok(k) = (k!=9) && (Mod(sigma(k), k-9) == 0); \\ Michel Marcus, May 30 2025

Crossrefs

Contains subsequence A223608.

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

Sequence in context: A063971 A191879 A097069 * A031237 A031314 A209723

Adjacent sequences: A274561 A274562 A274563 * A274565 A274566 A274567

Keyword

nonn,more

Author

Paolo P. Lava, Jul 06 2016

Extensions

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

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

a(14) from Max Alekseyev, Jan 30 2026

Status

approved