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 A307817 a(1) = 1; a(n+1) = Sum_{d|n} sigma(n/d)*a(d), where sigma = sum of divisors (A000203). 1
 1, 1, 4, 8, 18, 24, 52, 60, 106, 135, 213, 225, 397, 411, 599, 719, 1001, 1019, 1533, 1553, 2192, 2464, 3151, 3175, 4502, 4641, 5888, 6404, 8145, 8175, 11040, 11072, 13863, 14811, 17886, 18390, 23723, 23761, 28440, 30140, 36650, 36692, 45952, 45996, 55095, 58535, 68084, 68132, 83720, 84193 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS FORMULA G.f. A(x) satisfies: A(x) = x * (1 + Sum_{k>=1} sigma(k)*A(x^k)). G.f.: A(x) = Sum_{n>=1} a(n)*x^n = x * (1 + Sum_{i>=1} Sum_{j>=1} sigma(i)*a(j)*x^(i*j)). MATHEMATICA a[n_] := a[n] = Sum[DivisorSigma[1, (n - 1)/d] a[d] , {d, Divisors[n - 1]}]; a[1] = 1; Table[a[n], {n, 1, 50}] terms = 50; A[_] = 0; Do[A[x_] = x (1 + Sum[DivisorSigma[1, k]  A[x^k], {k, 1, terms}]) + O[x]^(terms + 1) // Normal, terms + 1]; Rest[CoefficientList[A[x], x]] a[n_] := a[n] = SeriesCoefficient[x (1 + Sum[Sum[DivisorSigma[1, i] a[j] x^(i j), {j, 1, n - 1}], {i, 1, n - 1}]), {x, 0, n}]; Table[a[n], {n, 1, 50}] PROG (PARI) lista(nn) = { my(va=vector(nn)); va[1] = 1; for (n=2, nn, va[n] = sumdiv(n-1, d, sigma((n-1)/d)*va[d])); va; } \\ Michel Marcus, Apr 30 2019 CROSSREFS Cf. A000203, A007557, A307794. Sequence in context: A308150 A070213 A077474 * A210433 A182099 A318756 Adjacent sequences:  A307814 A307815 A307816 * A307818 A307819 A307820 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Apr 30 2019 STATUS approved

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Last modified April 6 08:44 EDT 2020. Contains 333268 sequences. (Running on oeis4.)