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
Keywords
Examples
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.
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..1000, corrected by _Sidney Cadot_, Feb 05 2023
Programs
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Mathematica
Select[Range[2000], Mod[DivisorSigma[1, #] - 12, #] == 0 &] (* Vincenzo Librandi, Mar 11 2014, corrected by Amiram Eldar, Jan 04 2023 *)
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PARI
isok(k) = Mod(sigma(k), k) == 12; \\ Michel Marcus, Jan 04 2023
Extensions
Initial term 1 added by Vincenzo Librandi, Mar 11 2014
Terms 6 and 11 inserted by Michel Marcus, Jan 04 2023