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
Keywords
Links
Programs
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Mathematica
a[n_] := Total@ CatalanNumber[FactorInteger[n][[;; , 2]]]; a[1] = 0; Array[a, 100] (* Amiram Eldar, May 15 2023 *)
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PARI
A000108(n) = (binomial(2*n, n)/(n+1)); A318475(n) = vecsum(apply(e -> A000108(e),factor(n)[,2]));