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 A360948 a(n) = Sum_{d|n} (n/d)^(d-1) * binomial(d+n/d-1,d). 0

%I #17 Jul 31 2023 02:25:21

%S 1,3,4,11,6,41,8,89,100,182,12,1088,14,723,2592,3697,18,11804,20,

%T 29289,30382,13037,24,246912,78776,58554,374248,687929,30,2567895,32,

%U 3431585,4640462,1182284,6265548,37037563,38,5246529,55878240,128618380,42,266983306,44

%N a(n) = Sum_{d|n} (n/d)^(d-1) * binomial(d+n/d-1,d).

%F G.f.: Sum_{k>0} (1/k) * (1/(1 - k * x^k)^k - 1).

%F If p is prime, a(p) = 1 + p.

%t a[n_] := DivisorSum[n, (n/#)^(#-1) * Binomial[# + n/# - 1, #] &]; Array[a, 50] (* _Amiram Eldar_, Jul 31 2023 *)

%o (PARI) a(n) = sumdiv(n, d, (n/d)^(d-1)*binomial(d+n/d-1, d));

%o (PARI) my(N=50, x='x+O('x^N)); Vec(sum(k=1, N, (1/(1-k*x^k)^k-1)/k))

%Y Cf. A338662, A360794.

%K nonn

%O 1,2

%A _Seiichi Manyama_, Feb 26 2023

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Last modified May 26 08:30 EDT 2024. Contains 372814 sequences. (Running on oeis4.)