A307794 a(1) = 1; a(n+1) = Sum_{d|n} sigma(d)*a(d), where sigma = sum of divisors (A000203).

1, 1, 4, 17, 123, 739, 8888, 71105, 1066698, 13867091, 249608380, 2995300561, 83868424715, 1174157946011, 28179790775372, 676314978609683, 20965764337966871, 377383758083403679, 14717966565266619443, 294359331305332388861, 12363091914824209940661, 395618941274374718172273

Offset

1,3

Links

Table of n, a(n) for n=1..22.

Formula

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

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

Mathematica

a[n_] := a[n] = Sum[DivisorSigma[1, d] a[d], {d, Divisors[n - 1]}]; a[1] = 1; Table[a[n], {n, 1, 22}]
a[n_] := a[n] = SeriesCoefficient[x (1 + Sum[DivisorSigma[1, k] a[k] x^k/(1 - x^k), {k, 1, n - 1}]), {x, 0, n}]; Table[a[n], {n, 1, 22}]

Prog

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

Crossrefs

Cf. A000203, A001001, A307793.

Sequence in context: A260694 A032115 A054927 * A071138 A337521 A032325

Adjacent sequences: A307791 A307792 A307793 * A307795 A307796 A307797

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 29 2019

Status

approved