A077255 Numbers k such that prime(k)^k == 1 (mod k).

2, 4, 5, 6, 8, 10, 12, 14, 16, 18, 20, 24, 27, 32, 36, 40, 42, 48, 50, 52, 54, 60, 64, 70, 72, 80, 84, 96, 100, 105, 108, 110, 114, 120, 121, 124, 125, 126, 128, 136, 144, 148, 156, 160, 162, 168, 180, 181, 182, 189, 192, 200, 210, 216, 220, 231, 234, 240, 243, 246

Offset

1,1

Comments

Contains A023143. All terms not in A023143 are in A060679. - Robert Israel, Oct 31 2016

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

A077254(a(n)) = 1; A077256(n) = A000040(a(n)).

Example

prime(16)^16 mod 16 = 53^16 mod 16 = 3876269050118516845397872321 mod 16 = 1, therefore 16 is a term.

Maple

select(n -> ithprime(n) &^ n mod n = 1, [$1..1000]); # Robert Israel, Oct 31 2016

Mathematica

Select[Range[1000], PowerMod[Prime[#], #, #] == 1&] (* Jean-François Alcover, Dec 16 2021 *)

Prog

(PARI) isok(k) = lift(Mod(prime(k), k)^k) == 1; \\ Michel Marcus, Dec 16 2021

Crossrefs

Cf. A000040, A023143, A060679, A077254, A077256.

Sequence in context: A324694 A249025 A065502 * A262439 A331903 A371447

Adjacent sequences: A077252 A077253 A077254 * A077256 A077257 A077258

Keyword

nonn

Author

Reinhard Zumkeller, Oct 31 2002

Status

approved