A318471 Additive with a(p^e) = A000045(e).

0, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2, 3, 1, 2, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 1, 3, 1, 5, 2, 2, 2, 2, 1, 2, 2, 3, 1, 3, 1, 2, 2, 2, 1, 4, 1, 2, 2, 2, 1, 3, 2, 3, 2, 2, 1, 3, 1, 2, 2, 8, 2, 3, 1, 2, 2, 3, 1, 3, 1, 2, 2, 2, 2, 3, 1, 4, 3, 2, 1, 3, 2, 2, 2, 3, 1, 3, 2, 2, 2, 2, 2, 6, 1, 2, 2, 2, 1, 3, 1, 3, 3

Offset: 1

Author

Antti Karttunen, Aug 29 2018

Keywords

• nonn
• easy

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences computed from exponents in factorization of n.

Crossrefs

Cf. A000045, A077761, A318472, A318473.

Programs

Mathematica

a[n_] := Total@ Fibonacci[FactorInteger[n][[;; , 2]]]; a[1] = 0; Array[a, 100] (* Amiram Eldar, May 15 2023 *)

PARI

A318471(n) = vecsum(apply(e -> fibonacci(e),factor(n)[,2]));

Formula

a(n) = A007814(A318472(n)).

Sum_{k=1..n} a(k) ~ n * (log(log(n)) + B + C), where B is Mertens's constant (A077761) and C = Sum_{k>=3} Fibonacci(k-2) * P(k) = 0.58264195290963042938..., where P(s) is the prime zeta function. - Amiram Eldar, Oct 09 2023