A327275
a(1) = 1; a(n) = Sum_{d|n, dA001615.
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
Keywords
Programs
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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
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.