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%I #10 May 15 2023 08:46:21
%S 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,
%T 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,
%U 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
%N Additive with a(p^e) = A000108(e).
%H Antti Karttunen, <a href="/A318475/b318475.txt">Table of n, a(n) for n = 1..65537</a>
%H <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>.
%F a(n) = A007814(A318476(n)).
%t a[n_] := Total@ CatalanNumber[FactorInteger[n][[;; , 2]]]; a[1] = 0; Array[a, 100] (* _Amiram Eldar_, May 15 2023 *)
%o (PARI)
%o A000108(n) = (binomial(2*n, n)/(n+1));
%o A318475(n) = vecsum(apply(e -> A000108(e),factor(n)[,2]));
%Y Cf. A000108, A318476.
%K nonn
%O 1,4
%A _Antti Karttunen_, Aug 29 2018