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 A360948 a(n) = Sum_{d|n} (n/d)^(d-1) * binomial(d+n/d-1,d). 0
 1, 3, 4, 11, 6, 41, 8, 89, 100, 182, 12, 1088, 14, 723, 2592, 3697, 18, 11804, 20, 29289, 30382, 13037, 24, 246912, 78776, 58554, 374248, 687929, 30, 2567895, 32, 3431585, 4640462, 1182284, 6265548, 37037563, 38, 5246529, 55878240, 128618380, 42, 266983306, 44 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Table of n, a(n) for n=1..43. FORMULA G.f.: Sum_{k>0} (1/k) * (1/(1 - k * x^k)^k - 1). If p is prime, a(p) = 1 + p. MATHEMATICA a[n_] := DivisorSum[n, (n/#)^(#-1) * Binomial[# + n/# - 1, #] &]; Array[a, 50] (* Amiram Eldar, Jul 31 2023 *) PROG (PARI) a(n) = sumdiv(n, d, (n/d)^(d-1)*binomial(d+n/d-1, d)); (PARI) my(N=50, x='x+O('x^N)); Vec(sum(k=1, N, (1/(1-k*x^k)^k-1)/k)) CROSSREFS Cf. A338662, A360794. Sequence in context: A328851 A197953 A198299 * A175317 A056045 A360794 Adjacent sequences: A360945 A360946 A360947 * A360949 A360950 A360951 KEYWORD nonn AUTHOR Seiichi Manyama, Feb 26 2023 STATUS approved

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Last modified April 23 09:22 EDT 2024. Contains 371905 sequences. (Running on oeis4.)