A045835 - OEIS

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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

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OFFSET

1,2

COMMENTS

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

squares of primes (A001248) are a subsequence.

LINKS

Table of n, a(n) for n=1..58.

EXAMPLE

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.

MATHEMATICA

sopfr[n_] := If[n == 1, 0, Total[Times @@@ FactorInteger[n]]];