OFFSET
1,3
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
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Apr 30 2019
STATUS
approved