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

1,2

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]]];
Select[Range[1000], If[# == 1, True, sopfr[PrimeOmega[#]] == PrimeOmega[sopfr[#]]]&] (* Jean-François Alcover, Apr 06 2021 *)

Crossrefs

Cf. A001222, A001414, A001248, A076361.

Sequence in context: A313015 A313016 A313017 * A313018 A313019 A313020

Adjacent sequences: A045832 A045833 A045834 * A045836 A045837 A045838

Keyword

nonn

Author

Reinhard Zumkeller, Mar 04 2003

Status

approved