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

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)
A000108(n) = (binomial(2*n, n)/(n+1));
A318475(n) = vecsum(apply(e -> A000108(e), factor(n)[, 2]));

Crossrefs

Cf. A000108, A318476.

Sequence in context: A128515 A332489 A119569 * A066083 A128644 A201733

Adjacent sequences: A318472 A318473 A318474 * A318476 A318477 A318478

Keyword

nonn

Author

Antti Karttunen, Aug 29 2018

Status

approved