A125071 a(n) = sum of the exponents in the prime factorization of n which are not primes.

0, 1, 1, 0, 1, 2, 1, 0, 0, 2, 1, 1, 1, 2, 2, 4, 1, 1, 1, 1, 2, 2, 1, 1, 0, 2, 0, 1, 1, 3, 1, 0, 2, 2, 2, 0, 1, 2, 2, 1, 1, 3, 1, 1, 1, 2, 1, 5, 0, 1, 2, 1, 1, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 6, 2, 3, 1, 1, 2, 3, 1, 0, 1, 2, 1, 1, 2, 3, 1, 5, 4, 2, 1, 2, 2, 2, 2, 1, 1, 2, 2, 1, 2, 2, 2, 1, 1, 1, 1, 0, 1, 3, 1, 1, 3

Offset: 1

Author

Leroy Quet, Nov 18 2006

Keywords

• nonn
• easy

Examples

			720 has the prime-factorization of 2^4 *3^2 *5^1. Two of these exponents, 4 and 1, aren't primes. So a(720) = 4 + 1 = 5.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Index entries for sequences computed from exponents in factorization of n.

Crossrefs

Cf. A001222, A077761, A191558, A125070.

Programs

Mathematica

f[n_] := Plus @@ Select[Last /@ FactorInteger[n], ! PrimeQ[ # ] &];Table[f[n], {n, 110}] (* Ray Chandler, Nov 19 2006 *)

PARI

A125071(n) = vecsum(apply(e -> if(isprime(e),0,e), factorint(n)[, 2])); \\ Antti Karttunen, Jul 07 2017

Formula

From Amiram Eldar, Sep 30 2023: (Start)

Additive with a(p^e) = A191558(e).

Sum_{k=1..n} a(k) ~ n * (log(log(n)) + B - C), where B is Mertens's constant (A077761) and C = Sum_{p prime} p * (P(p) - P(p+1)) - Sum_{k>=2} P(k) = 0.20171354082810650948..., where P(s) is the prime zeta function. (End)

Extensions

Extended by Ray Chandler, Nov 19 2006