A342956 a(n) = A001222(A001414(n)).

0, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 3, 3, 1, 3, 1, 2, 2, 1, 1, 2, 2, 2, 2, 1, 1, 2, 1, 2, 2, 1, 3, 2, 1, 2, 4, 1, 1, 3, 1, 2, 1, 2, 1, 1, 2, 3, 3, 1, 1, 1, 4, 1, 2, 1, 1, 3, 1, 2, 1, 3, 3, 4, 1, 2, 2, 2, 1, 3, 1, 2, 1, 1, 3, 3, 1, 1, 3, 1, 1, 2, 2, 3, 5, 1, 1, 1, 3, 3, 2, 2, 4, 1, 1, 4, 1

Offset: 1

Author

J. M. Bergot and Robert Israel, Mar 30 2021

Keywords

• nonn

Comments

a(n) is the number of prime divisors of the sum of prime divisors of n, counting multiplicity in both cases.

Examples

			a(16) = 3 because A001414(16) = 2+2+2+2 = 8 and A001222(8) = A001222(2^3) = 3.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001222, A001414, A342957.

Programs

Maple

f:= proc(n) local t; numtheory:-bigomega(add(t[1]*t[2],t=ifactors(n)[2])) end proc:
map(f, [$1..100]);

Mathematica

Array[PrimeOmega[Plus@@Times@@@FactorInteger@#]&,100] (* Giorgos Kalogeropoulos, Mar 31 2021 *)

Python

from sympy import factorint
def A342956(n): return sum(factorint(sum(p*e for p, e in factorint(n).items())).values()) if n > 1 else 0 # Chai Wah Wu, Mar 31 2021