A327275 a(1) = 1; a(n) = Sum_{d|n, d<n} psi(n/d) * a(d), where psi = A001615.

1, 3, 4, 15, 6, 36, 8, 75, 28, 54, 12, 252, 14, 72, 72, 375, 18, 348, 20, 378, 96, 108, 24, 1620, 66, 126, 196, 504, 30, 936, 32, 1875, 144, 162, 144, 3108, 38, 180, 168, 2430, 42, 1248, 44, 756, 696, 216, 48, 9900, 120, 810, 216, 882, 54, 3108, 216, 3240, 240, 270, 60, 8568

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} psi(k) * A(x^k).

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

Mathematica

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

Crossrefs

Cf. A001615, A006874, A048250, A323363.

Sequence in context: A130409 A365349 A258468 * A343939 A157351 A071167

Adjacent sequences: A327272 A327273 A327274 * A327276 A327277 A327278

Keyword

nonn

Author

Ilya Gutkovskiy, Sep 15 2019

Status

approved