A056741 Numbers k such that k | 5^k + 4^k + 3^k + 2^k + 1^k.

1, 3, 5, 9, 15, 25, 27, 45, 75, 81, 125, 135, 225, 243, 261, 295, 375, 405, 625, 675, 729, 925, 1125, 1215, 1875, 2025, 2187, 3125, 3375, 3645, 4077, 4833, 5139, 5625, 6075, 6345, 6561, 9375, 10125, 10935, 15625, 16875, 17895, 18125, 18225, 18495, 19683

Offset: 1

Author

Robert G. Wilson v, Aug 25 2000

Keywords

• nonn

Comments

All terms are odd. The only primes in the sequence are 3 and 5. - Robert Israel, Jun 25 2025

Links

• Robert Israel, Table of n, a(n) for n = 1..300 (first 100 terms from Harvey P. Dale)

Crossrefs

Cf. A001552, A056739, A057291, A057292.

Programs

Maple

filter:= n ->   5&^n + 4&^n + 3&^n + 2&^n + 1 mod n = 0:
select(filter, [seq(i,i=1..10^5,2)]); # Robert Israel, Jun 25 2025

Mathematica

Do[ If[ Mod[ PowerMod[ 5, n, n ] + PowerMod[ 4, n, n ] + PowerMod[ 3, n, n ] + PowerMod[ 2, n, n ] + 1, n ] == 0, Print[ n ] ], {n, 1, 10^6} ]
Select[Range[20000],Mod[Total[PowerMod[Range[0,5],#,#]],#]==0&] (* Harvey P. Dale, Oct 09 2021 *)