A359188 a(n) = Sum_{d|n} mu(n/d) * d * (n/d)^(d-1), where mu() is the Moebius function (A008683).
1, 1, 2, 0, 4, -11, 6, -24, -18, -79, 10, -276, 12, -447, -464, -1008, 16, -3636, 18, -5580, -5228, -11263, 22, -41184, -3100, -53247, -59022, -116004, 28, -454501, 30, -524256, -649868, -1114111, -121344, -4438368, 36, -4980735, -6909200, -11106720, 40, -44114197, 42
Offset: 1
Keywords
Programs
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Mathematica
a[n_] := DivisorSum[n, MoebiusMu[n/#] * # * (n/#)^(#-1) &]; Array[a, 45] (* Amiram Eldar, Aug 27 2023 *)
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PARI
a(n) = sumdiv(n, d, moebius(n/d)*d*(n/d)^(d-1));
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PARI
my(N=50, x='x+O('x^N)); Vec(sum(k=1, N, moebius(k)*x^k/(1-k*x^k)^2))
Formula
G.f.: Sum_{k>=1} mu(k) * x^k/(1 - k * x^k)^2.
If p is prime, a(p) = p - 1.