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A076496
Numbers k such that sigma(k) == 12 (mod k).
11
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. A141545 (a subsequence).
Sequence in context: A362442 A372999 A063629 * A354594 A219628 A093027
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