A076496 - OEIS

%I #48 Feb 05 2023 08:15:10

%S 1,6,11,24,30,42,54,66,78,102,114,121,138,174,186,222,246,258,282,304,

%T 318,354,366,402,426,438,474,498,534,582,606,618,642,654,678,762,780,

%U 786,822,834,894,906,942,978,1002,1038,1074,1086,1146,1158,1182,1194,1266,1338

%N Numbers k such that sigma(k) == 12 (mod k).

%H Vincenzo Librandi, <a href="/A076496/b076496.txt">Table of n, a(n) for n = 1..1000</a>, corrected by _Sidney Cadot_, Feb 05 2023

%e 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.

%t Select[Range[2000], Mod[DivisorSigma[1, #] - 12, #] == 0 &] (* _Vincenzo Librandi_, Mar 11 2014, corrected by _Amiram Eldar_, Jan 04 2023 *)

%o (PARI) isok(k) = Mod(sigma(k), k) == 12; \\ _Michel Marcus_, Jan 04 2023

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

%Y Cf. A141545 (a subsequence).

%K nonn

%O 1,2

%A _Labos Elemer_, Oct 21 2002

%E Initial term 1 added by _Vincenzo Librandi_, Mar 11 2014

%E Terms 6 and 11 inserted by _Michel Marcus_, Jan 04 2023