A045835 Numbers n such that sopfr(Omega(n)) = Omega(sopfr(n)), where Omega(m) is the number and sopfr(m) is the sum of prime factors of m, with repetition respectively.

1, 4, 9, 14, 18, 21, 25, 26, 33, 38, 42, 46, 49, 50, 57, 62, 69, 74, 78, 85, 92, 93, 94, 106, 110, 121, 129, 130, 133, 134, 138, 140, 145, 154, 164, 166, 169, 177, 178, 189, 204, 205, 213, 217, 218, 222, 225, 226, 230, 236, 237, 249, 253, 254, 262, 265, 266, 278

Offset: 1

Author

Reinhard Zumkeller, Mar 04 2003

Keywords

• nonn

Comments

A001414(A001222(a(n))) = A001222(A001414(a(n)));

squares of primes (A001248) are a subsequence.

Examples

			n=189=3*3*3*7: Omega(sopfr(189))=Omega(3+3+3+7)=Omega(16)=4, sopfr(Omega(189))=sopfr(4)=2+2=4, therefore 189 is a term.
		

Crossrefs

Cf. A001222, A001414, A001248, A076361.

Programs

Mathematica

sopfr[n_] := If[n == 1, 0, Total[Times @@@ FactorInteger[n]]];
Select[Range[1000], If[# == 1, True, sopfr[PrimeOmega[#]] == PrimeOmega[sopfr[#]]]&] (* Jean-François Alcover, Apr 06 2021 *)