A125071 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,6

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000

Index entries for sequences computed from exponents in factorization of n.

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)

EXAMPLE

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.

MATHEMATICA

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

PROG

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

CROSSREFS

Cf. A001222, A077761, A191558, A125070.

Sequence in context: A341595 A369428 A125070 * A335699 A177207 A161528

Adjacent sequences: A125068 A125069 A125070 * A125072 A125073 A125074

KEYWORD

nonn,easy

AUTHOR

Leroy Quet, Nov 18 2006

EXTENSIONS

Extended by Ray Chandler, Nov 19 2006

STATUS

approved