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%I #37 Nov 07 2018 10:04:05
%S 1,5,28,17,3126,47450,823544,257,19684,10009766650,285311670612,
%T 2177317874,302875106592254,11112685048647250,437893920912786408,
%U 65537,827240261886336764178,101560344351050,1978419655660313589123980,100000095367432689202
%N a(n) = Sum_{d|n} mu(d)^2*d^n.
%H Seiichi Manyama, <a href="/A321236/b321236.txt">Table of n, a(n) for n = 1..388</a>
%F G.f.: Sum_{k>=1} mu(k)^2*(k*x)^k/(1 - (k*x)^k).
%F a(n) = Product_{p|n, p prime} (1 + p^n).
%t Table[Sum[MoebiusMu[d]^2 d^n, {d, Divisors[n]}], {n, 20}]
%t nmax = 20; Rest[CoefficientList[Series[Sum[MoebiusMu[k]^2 (k x)^k/(1 - (k x)^k), {k, 1, nmax}], {x, 0, nmax}], x]]
%t Table[Product[1 + Boole[PrimeQ[d]] d^n, {d, Divisors[n]}], {n, 20}]
%o (PARI) a(n) = sumdiv(n, d, moebius(d)^2*d^n) \\ _Andrew Howroyd_, Nov 06 2018
%Y Cf. A008683, A048250, A320974, A321222.
%K nonn
%O 1,2
%A _Ilya Gutkovskiy_, Nov 06 2018
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