A076496 Numbers k such that sigma(k) == 12 (mod k).

1, 6, 11, 24, 30, 42, 54, 66, 78, 102, 114, 121, 138, 174, 186, 222, 246, 258, 282, 304, 318, 354, 366, 402, 426, 438, 474, 498, 534, 582, 606, 618, 642, 654, 678, 762, 780, 786, 822, 834, 894, 906, 942, 978, 1002, 1038, 1074, 1086, 1146, 1158, 1182, 1194, 1266, 1338

Offset

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000, corrected by Sidney Cadot, Feb 05 2023

Example

6*p is a solution if p > 3 is prime, since sigma(6*p) = 1 + 2 + 3 + 6 + p + 2*p + 3*p + 6*p = 12*(p+1) = 2*6*p + 12 = 2*k + 12. These are "regular" solutions. Also k = 121, 304 are "singular" solutions. See other remainders in cross-references.

Mathematica

Select[Range[2000], Mod[DivisorSigma[1, #] - 12, #] == 0 &] (* Vincenzo Librandi, Mar 11 2014, corrected by Amiram Eldar, Jan 04 2023 *)

Prog

(PARI) isok(k) = Mod(sigma(k), k) == 12; \\ Michel Marcus, Jan 04 2023

Crossrefs

Cf. A054024, A045768, A045769, A045770, A076495, A088834.

Cf. A141545 (a subsequence).

Sequence in context: A362442 A372999 A063629 * A354594 A219628 A093027

Adjacent sequences: A076493 A076494 A076495 * A076497 A076498 A076499

Keyword

nonn

Author

Labos Elemer, Oct 21 2002

Extensions

Initial term 1 added by Vincenzo Librandi, Mar 11 2014

Terms 6 and 11 inserted by Michel Marcus, Jan 04 2023

Status

approved