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%I #25 Sep 30 2023 21:55:41
%S 0,1,1,2,1,2,1,3,2,2,1,3,1,2,2,0,1,3,1,3,2,2,1,4,2,2,3,3,1,3,1,5,2,2,
%T 2,4,1,2,2,4,1,3,1,3,3,2,1,1,2,3,2,3,1,4,2,4,2,2,1,4,1,2,3,0,2,3,1,3,
%U 2,3,1,5,1,2,3,3,2,3,1,1,0,2,1,4,2,2,2,4,1,4,2,3,2,2,2,6,1,3,3,4,1,3,1,4,3
%N a(n) = sum of exponents in the prime factorization of n that are noncomposite.
%H Antti Karttunen, <a href="/A125030/b125030.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>.
%F From _Amiram Eldar_, Sep 30 2023: (Start)
%F Additive with a(p^e) = e if e is composite, and 0 otherwise.
%F Sum_{k=1..n} a(k) ~ n * (log(log(n)) + B + C), where B is Mertens's constant (A077761) and C = - P(2) + Sum_{p prime} p * (P(p) - P(p+1)) = 0.52262278983683613884..., where P(s) is the prime zeta function. (End)
%e a(720) = 3, since the prime factorization of 720 is 2^4 * 3^2 * 5^1 and two of the exponents in this factorization are noncomposites (the exponents 2 and 1, whose sum is 3).
%t f[n_] := Plus @@ Select[Last /@ FactorInteger[n], # == 1 || PrimeQ[ # ] &];Table[f[n], {n, 110}] (* _Ray Chandler_, Nov 19 2006 *)
%o (PARI) A125030(n) = vecsum(apply(e -> if((1==e)||isprime(e),e,0), factorint(n)[, 2])); \\ _Antti Karttunen_, Jul 07 2017
%Y Cf. A077761, A001222, A125029, A125071.
%K nonn,easy
%O 1,4
%A _Leroy Quet_, Nov 16 2006
%E Extended by _Ray Chandler_, Nov 19 2006
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