A307653 a(n) = Sum_{d|n} mu(d) * d^d.
1, -3, -26, -3, -3124, 46626, -823542, -3, -26, 9999996872, -285311670610, 46626, -302875106592252, 11112006824734470, 437893890380856224, -3, -827240261886336764176, 46626, -1978419655660313589123978, 9999996872, 5842587018385982521380300852
Offset: 1
Keywords
Examples
a(6) = 1 - 2^2 - 3^3 + 6^6 = 46626.
Links
- Seiichi Manyama, Table of n, a(n) for n = 1..388
Programs
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Mathematica
Array[DivisorSum[#, MoebiusMu[#]*#^# &] &, 21] (* Michael De Vlieger, Apr 21 2019 *)
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PARI
{a(n) = sumdiv(n, d, moebius(d)*d^d)}
Formula
a(prime(n)^m) = 1 - prime(n)^prime(n) = -A088730(n) for m > 0.
G.f.: Sum_{k>=1} mu(k)*k^k*x^k/(1 - x^k). - Ilya Gutkovskiy, Apr 20 2019