A384369 Numbers k such that Omega(k)^Omega(k) == Omega(k) (mod k) where Omega = A001222.

1, 2, 3, 5, 7, 8, 11, 12, 13, 17, 19, 23, 29, 31, 36, 37, 41, 43, 47, 48, 53, 59, 61, 67, 71, 73, 79, 80, 83, 84, 89, 97, 101, 103, 107, 109, 113, 120, 126, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 208, 211, 223, 227, 229, 233, 239, 241

Offset: 1

Author

Juri-Stepan Gerasimov, May 30 2025

Keywords

• nonn
• changed

Examples

			8 is a term because Omega(8)^Omega(8) = 3^3 = 27 == 3 (mod 8).
		

Crossrefs

Supersequence of primes A000040.

Cf. A001222.

Programs

Magma

[k: k in [1..250] | (k eq 1 select 0 else &+[p[2]: p in Factorization(k)])^(k eq 1 select 0 else &+[p[2]: p in Factorization(k)]) mod k eq (k eq 1 select 0 else &+[p[2]: p in Factorization(k)])];

Mathematica

{1}~Join~Select[Range[2,241],Mod[PrimeOmega[#]^PrimeOmega[#],#]==PrimeOmega[#]&] (* James C. McMahon, Jun 04 2025 *)