A378696 Numbers k such that omega(k)^k == omega(k) (mod k), where omega = A001221.

1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 23, 25, 27, 29, 31, 32, 37, 41, 43, 47, 49, 53, 59, 61, 64, 66, 67, 71, 73, 79, 81, 83, 89, 97, 101, 103, 107, 109, 113, 121, 125, 127, 128, 131, 137, 139, 149, 151, 157, 163, 167, 169, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 243

Offset

1,2

Comments

The sequence without A000961 and A001567 is 2665, 3367, 5551, 7107, 8205, 11011, 15457, 16471, 19345 ,... (see A379056).

Links

Table of n, a(n) for n=1..70.

Maple

filter:= proc(k) local w;
  w:= nops(numtheory:-factorset(k));
  w &^k - w mod k = 0
end proc:
select(filter, [$1..1000]); # Robert Israel, Dec 08 2024

Mathematica

q[k_] := Module[{om = PrimeNu[k]}, PowerMod[om, k, k] == om]; Select[Range[250], q] (* Amiram Eldar, Dec 06 2024 *)

Prog

(Magma) [k: k in [1..250] | #PrimeDivisors(k)^k mod k eq #PrimeDivisors(k)];
(PARI) isok(k) = my(x=omega(k)); Mod(x, k)^k == Mod(x, k); \\ Michel Marcus, Dec 04 2024

Crossrefs

Supersequence of A000961 and A002997.

Cf. A001221, A001567, A214305, A379056.

Sequence in context: A371445 A325371 A373071 * A059046 A363727 A329366

Adjacent sequences: A378693 A378694 A378695 * A378697 A378698 A378699

Keyword

nonn

Author

Juri-Stepan Gerasimov, Dec 04 2024

Status

approved