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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.
2
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
1,2
COMMENTS
A001414(A001222(a(n))) = A001222(A001414(a(n)));
squares of primes (A001248) are a subsequence.
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]]];
Select[Range[1000], If[# == 1, True, sopfr[PrimeOmega[#]] == PrimeOmega[sopfr[#]]]&] (* Jean-François Alcover, Apr 06 2021 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Mar 04 2003
STATUS
approved