A318473 Additive with a(p^e) = A000045(e+1).

0, 1, 1, 2, 1, 2, 1, 3, 2, 2, 1, 3, 1, 2, 2, 5, 1, 3, 1, 3, 2, 2, 1, 4, 2, 2, 3, 3, 1, 3, 1, 8, 2, 2, 2, 4, 1, 2, 2, 4, 1, 3, 1, 3, 3, 2, 1, 6, 2, 3, 2, 3, 1, 4, 2, 4, 2, 2, 1, 4, 1, 2, 3, 13, 2, 3, 1, 3, 2, 3, 1, 5, 1, 2, 3, 3, 2, 3, 1, 6, 5, 2, 1, 4, 2, 2, 2, 4, 1, 4, 2, 3, 2, 2, 2, 9, 1, 3, 3, 4, 1, 3, 1, 4, 3

Offset

1,4

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

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

Formula

a(n) = A007814(A318474(n)).

Sum_{k=1..n} a(k) ~ n * (log(log(n)) + B + C), where B is Mertens's constant (A077761) and C = Sum_{k>=2} Fibonacci(k-1) * P(k) = 1.30985781707683753402..., where P(s) is the prime zeta function. - Amiram Eldar, Oct 09 2023

Mathematica

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

Prog

(PARI) A318473(n) = vecsum(apply(e -> fibonacci(1+e), factor(n)[, 2]));

Crossrefs

Cf. A000045, A077761, A318471, A318474.

Differs from A008481 for the first time at n=32, where a(32)=8, while A008481(32)=7.

Sequence in context: A329378 A329617 A008481 * A127669 A323436 A056692

Adjacent sequences: A318470 A318471 A318472 * A318474 A318475 A318476

Keyword

nonn,easy

Author

Antti Karttunen, Aug 29 2018

Status

approved