A307793 - OEIS

A307793

a(1) = 1; a(n+1) = Sum_{d|n} tau(d)*a(d), where tau = number of divisors (A000005).

1, 1, 3, 7, 24, 49, 205, 411, 1668, 5011, 20095, 40191, 241372, 482745, 1931393, 7725627, 38629803, 77259607, 463562851, 927125703, 5562774334, 22251097753, 89004431205, 178008862411, 1424071142304, 4272213426961, 17088854190591, 68355416767375, 410132502535664, 820265005071329

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OFFSET

1,3

LINKS

Table of n, a(n) for n=1..30.

FORMULA

G.f.: x * (1 + Sum_{n>=1} tau(n)*a(n)*x^n/(1 - x^n)).

L.g.f.: -log(Product_{i>=1, j>=1} (1 - x^(i*j))^(a(i*j)/(i*j))) = Sum_{n>=1} a(n+1)*x^n/n.

MATHEMATICA

a[n_] := a[n] = Sum[DivisorSigma[0, d] a[d], {d, Divisors[n - 1]}]; a[1] = 1; Table[a[n], {n, 1, 30}]

a[n_] := a[n] = SeriesCoefficient[x (1 + Sum[DivisorSigma[0, k] a[k] x^k/(1 - x^k), {k, 1, n - 1}]), {x, 0, n}]; Table[a[n], {n, 1, 30}]

PROG

(PARI) a(n) = if (n==1, 1, sumdiv(n-1, d, numdiv(d)*a(d))); \\ Michel Marcus, Apr 29 2019

CROSSREFS

Cf. A000005, A007557, A060640, A307794, A319133.

Sequence in context: A358974 A110864 A046102 * A145542 A071108 A148713

Adjacent sequences: A307790 A307791 A307792 * A307794 A307795 A307796

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Apr 29 2019

STATUS

approved