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 A125070 a(n) = number of nonzero exponents in the prime factorization of n which are not primes. 9
 0, 1, 1, 0, 1, 2, 1, 0, 0, 2, 1, 1, 1, 2, 2, 1, 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, 2, 0, 1, 2, 1, 1, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 1, 2, 3, 1, 1, 2, 3, 1, 0, 1, 2, 1, 1, 2, 3, 1, 2, 1, 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) = A005171(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+1)) = 0.39847584805803104040..., 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, are not primes. So a(720) = 2. MATHEMATICA f[n_] := Length @ Select[Last /@ FactorInteger[n], ! PrimeQ[ # ] &]; Table[f[n], {n, 110}] (* Ray Chandler, Nov 19 2006 *) PROG (PARI) A125070(n) = vecsum(apply(e -> if(isprime(e), 0, 1), factorint(n)[, 2])); \\ Antti Karttunen, Jul 07 2017 CROSSREFS Cf. A001221, A005171, A077761, A125071. Sequence in context: A286852 A341595 A369428 * A125071 A335699 A177207 Adjacent sequences: A125067 A125068 A125069 * A125071 A125072 A125073 KEYWORD nonn,easy AUTHOR Leroy Quet, Nov 18 2006 EXTENSIONS Extended by Ray Chandler, Nov 19 2006 STATUS approved

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Last modified September 17 14:32 EDT 2024. Contains 375987 sequences. (Running on oeis4.)