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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 (list; graph; refs; listen; history; text; internal format)
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: A309742 A362442 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

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)