OFFSET
1,2
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
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Sep 15 2019
STATUS
approved