A343977 Numbers k such that k | 11^k + 7^k + 5^k + 3^k + 2^k.

1, 2, 4, 7, 26, 49, 338, 343, 2401, 4394, 7076, 15043, 16807, 17764, 57122, 117649, 226723, 241484, 295687, 742586, 818974, 823543, 826973, 1456511, 2040506, 2806769, 3472189, 5764801, 6321233, 9653618, 32036249, 40353607, 89758063, 107884133, 125497034, 126090551, 132590423

Offset: 1

Author

Zak Seidov, May 06 2021

Keywords

• nonn

Comments

This sequence is infinite as it contains 7^n. - David A. Corneth, May 06 2021

Crossrefs

Cf. A000420, A045576, A220170.

Programs

Maple

q:= k-> is(0=11&^k+7&^k+5&^k+3&^k+2&^k mod k):
select(q, [$1..100000])[];  # Alois P. Heinz, May 06 2021

Mathematica

q[k_] := Divisible[Plus @@ (PowerMod[#, k, k] & /@ {2, 3, 5, 7, 11}), k]; Select[Range[10^6], q] (* Amiram Eldar, May 06 2021 *)

PARI

is(n) = lift(Mod(11, n)^n + Mod(7, n)^n + Mod(5, n)^n + Mod(3, n)^n + Mod(2, n)^n) == 0 \\ David A. Corneth, May 06 2021

Extensions

a(24)-a(37) from Alois P. Heinz, May 06 2021