A318475 - OEIS

A318475

Additive with a(p^e) = A000108(e).

0, 1, 1, 2, 1, 2, 1, 5, 2, 2, 1, 3, 1, 2, 2, 14, 1, 3, 1, 3, 2, 2, 1, 6, 2, 2, 5, 3, 1, 3, 1, 42, 2, 2, 2, 4, 1, 2, 2, 6, 1, 3, 1, 3, 3, 2, 1, 15, 2, 3, 2, 3, 1, 6, 2, 6, 2, 2, 1, 4, 1, 2, 3, 132, 2, 3, 1, 3, 2, 3, 1, 7, 1, 2, 3, 3, 2, 3, 1, 15, 14, 2, 1, 4, 2, 2, 2, 6, 1, 4, 2, 3, 2, 2, 2, 43, 1, 3, 3, 4, 1, 3, 1, 6, 3

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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(A318476(n)).

MATHEMATICA

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

PROG

(PARI)