A325212 a(1) = 1; a(n) = Sum_{d|n, d<n} sigma(n/d) * a(d), where sigma = A000203.

1, 3, 4, 16, 6, 36, 8, 84, 29, 54, 12, 264, 14, 72, 72, 440, 18, 357, 20, 396, 96, 108, 24, 1776, 67, 126, 208, 528, 30, 936, 32, 2304, 144, 162, 144, 3290, 38, 180, 168, 2664, 42, 1248, 44, 792, 714, 216, 48, 11360, 121, 819, 216, 924, 54, 3264, 216, 3552, 240, 270, 60, 8880

Offset

1,2

Links

Table of n, a(n) for n=1..60.

Formula

G.f. A(x) satisfies: A(x) = x + Sum_{k>=2} sigma(k) * A(x^k).

a(p) = p + 1, where p is prime.

Mathematica

a[n_] := If[n == 1, n, Sum[If[d < n, DivisorSigma[1, n/d] a[d], 0], {d, Divisors[n]}]]; Table[a[n], {n, 1, 60}]
nmax = 60; A[_] = 0; Do[A[x_] = x + Sum[DivisorSigma[1, k] A[x^k], {k, 2, nmax}] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x] // Rest

Prog

(PARI) seq(n)={my(v=vector(n)); v[1]=1; for(n=2, #v, v[n] = sumdiv(n, d, v[d]*sigma(n/d))); v} \\ Andrew Howroyd, Sep 05 2019

Crossrefs

Cf. A000203, A046692, A307817, A325211.

Sequence in context: A103095 A041325 A042541 * A329890 A334319 A330299

Adjacent sequences: A325209 A325210 A325211 * A325213 A325214 A325215

Keyword

nonn

Author

Ilya Gutkovskiy, Sep 05 2019

Status

approved