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.

1, 2, 3, 9, 10, 13, 26, 27, 39, 50, 81, 110, 117, 130, 169, 243, 250, 279, 310, 338, 351, 470, 507, 550, 650, 663, 729, 1053, 1209, 1250, 1430, 1521, 1550, 1690, 2187, 2197, 2750, 3159, 3250, 3410, 4030, 4043, 4069, 4394, 4509, 4563, 6250, 6561, 6591, 7150

Offset

1,2

Comments

The only primes in the sequence are 2, 3 and 13. - Robert Israel, Jun 25 2025

Links

Robert Israel, Table of n, a(n) for n = 1..720

Maple

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:
select(filter, [$1..10^4]); # Robert Israel, Jun 25 2025

Mathematica

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 & ]
Select[Range[7200], Divisible[Total[Range[12]^#], #]&] (* Harvey P. Dale, Aug 05 2017 *)

Crossrefs

Cf. A056739, A057292, A103438.

Sequence in context: A357353 A214433 A257026 * A135107 A191568 A279549

Adjacent sequences: A057288 A057289 A057290 * A057292 A057293 A057294

Keyword

nonn

Author

Robert G. Wilson v, Sep 22 2000

Status

approved