A057292 Numbers k such that 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, 11, 22, 27, 33, 46, 81, 99, 121, 209, 242, 243, 297, 363, 729, 891, 1058, 1089, 1179, 1331, 1702, 2187, 2662, 2673, 3082, 3267, 3993, 6561, 8019, 9801, 11979, 14641, 19683, 20673, 24057, 24334, 25029, 29282, 29403, 30591, 30734

Offset: 1

Author

Robert G. Wilson v, Sep 22 2000

Keywords

• nonn

Comments

The only primes in the sequence are 2, 3 and 11. - Robert Israel, Jun 25 2025

Links

• Robert Israel, Table of n, a(n) for n = 1..227

Crossrefs

Cf. A056739, A057291, A103438.

Programs

Maple

filter:= 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..10^5]); # Robert Israel, Jun 25 2025

Mathematica

Select[ Range[ 10^5 ], Mod[ PowerMod[ 11, #, # ] + PowerMod[ 10, #, # ] + PowerMod[ 9, #, # ] + PowerMod[ 8, #, # ] + PowerMod[ 7, #, # ] + PowerMod[ 6, #, # ] + PowerMod[ 5, #, # ] + PowerMod[ 4, #, # ] + PowerMod[ 3, #, # ] + PowerMod[ 2, #, # ] + 1, # ] == 0 & ]
Select[Range[31000],Mod[Total[PowerMod[Range[0,11],#,#]],#]==0&] (* Harvey P. Dale, Nov 22 2021 *)