cp's OEIS Frontend

A057291 Numbers k such that k | 12^k + 11^k + 10^k + 9^k + 8^k + 7^k + 6^k + 5^k + 4^k + 3^k + 2^k + 1^k.

%I A057291 #16 Jun 25 2025 15:47:42
%S A057291 1,2,3,9,10,13,26,27,39,50,81,110,117,130,169,243,250,279,310,338,351,
%T A057291 470,507,550,650,663,729,1053,1209,1250,1430,1521,1550,1690,2187,2197,
%U A057291 2750,3159,3250,3410,4030,4043,4069,4394,4509,4563,6250,6561,6591,7150
%N A057291 Numbers k such that k | 12^k + 11^k + 10^k + 9^k + 8^k + 7^k + 6^k + 5^k + 4^k + 3^k + 2^k + 1^k.
%C A057291 The only primes in the sequence are 2, 3 and 13. - _Robert Israel_, Jun 25 2025
%H A057291 Robert Israel, <a href="/A057291/b057291.txt">Table of n, a(n) for n = 1..720</a>
%p A057291 filter:= n -> 12&^n + 11&^n + 10&^n + 9&^n + 8&^n + 7&^n + 6&^n + 5&^n + 4&^n + 3&^n + 2&^n + 1 mod n = 0:
%p A057291 select(filter, [$1..10^4]); # _Robert Israel_, Jun 25 2025
%t A057291 Select[ Range[ 10^5 ], Mod[ PowerMod[ 12, #, # ] + PowerMod[ 11, #, # ] + PowerMod[ 10, #, # ] + PowerMod[ 9, #, # ] + PowerMod[ 8, #, # ] + PowerMod[ 7, #, # ] + PowerMod[ 6, #, # ] + PowerMod[ 5, #, # ] + PowerMod[ 4, #, # ] + PowerMod[ 3, #, # ] + PowerMod[ 2, #, # ] + 1, # ] == 0 & ]
%t A057291 Select[Range[7200],Divisible[Total[Range[12]^#],#]&] (* _Harvey P. Dale_, Aug 05 2017 *)
%Y A057291 Cf. A056739, A057292, A103438.
%K A057291 nonn
%O A057291 1,2
%A A057291 _Robert G. Wilson v_, Sep 22 2000