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 A338658 a(n) = Sum_{d|n} d * binomial(d+n/d-1, d). 3
 1, 4, 6, 14, 10, 36, 14, 56, 48, 80, 22, 228, 26, 140, 240, 316, 34, 552, 38, 820, 546, 308, 46, 2088, 680, 416, 1044, 2156, 58, 4380, 62, 3248, 1782, 680, 4690, 9672, 74, 836, 2808, 14560, 82, 15456, 86, 9108, 17040, 1196, 94, 37704, 12110, 21420, 5916, 16068, 106, 44496 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Table of n, a(n) for n=1..54. FORMULA G.f.: Sum_{k >= 1} k * x^k/(1 - x^k)^(k+1). If p is prime, a(p) = 2*p. MATHEMATICA a[n_] := DivisorSum[n, # * Binomial[# + n/# - 1, #] &]; Array[a, 100] (* Amiram Eldar, Apr 22 2021 *) PROG (PARI) a(n) = sumdiv(n, d, d*binomial(d+n/d-1, d)); (PARI) my(N=66, x='x+O('x^N)); Vec(sum(k=1, N, k*x^k/(1-x^k)^(k+1))) CROSSREFS Cf. A081543, A343574. Sequence in context: A095867 A253535 A349171 * A344224 A310601 A310602 Adjacent sequences: A338655 A338656 A338657 * A338659 A338660 A338661 KEYWORD nonn AUTHOR Seiichi Manyama, Apr 22 2021 STATUS approved

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Last modified July 13 08:08 EDT 2024. Contains 374274 sequences. (Running on oeis4.)