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

1,4

Comments

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

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A001222, A001414, A342957.

Sequence in context: A319661 A378282 A320015 * A377907 A241918 A276317

Adjacent sequences: A342953 A342954 A342955 * A342957 A342958 A342959

Keyword

nonn

Author

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

Status

approved