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%I #20 Mar 12 2021 09:30:50
%S 1,9,83,1058,15629,282381,5764807,134480900,3486902505,100048836321,
%T 3138428376731,107006403495850,3937376385699301,155572843119518781,
%U 6568408661060858767,295150157013526773768,14063084452067724991025,708236697425777157039381
%N a(n) = Sum_{d|n} mu(n/d)*d*sigma_n(d).
%H Seiichi Manyama, <a href="/A321294/b321294.txt">Table of n, a(n) for n = 1..385</a>
%F a(n) = [x^n] Sum_{i>=1} Sum_{j>=1} mu(i)*j^(n+1)*x^(i*j)/(1 - x^(i*j))^2.
%F a(n) = Sum_{d|n} phi(n/d)*d^(n+1).
%F a(n) = Sum_{k=1..n} gcd(n,k)^(n+1).
%F a(n) ~ n^(n+1). - _Vaclav Kotesovec_, Nov 02 2018
%t Table[Sum[MoebiusMu[n/d] d DivisorSigma[n, d], {d, Divisors[n]}], {n, 18}]
%t Table[Sum[EulerPhi[n/d] d^(n + 1), {d, Divisors[n]}], {n, 18}]
%t Table[Sum[GCD[n, k]^(n + 1), {k, n}], {n, 18}]
%o (PARI) a(n) = sumdiv(n, d, moebius(n/d)*d*sigma(d, n)); \\ _Michel Marcus_, Nov 03 2018
%o (Python)
%o from sympy import totient, divisors
%o def A321294(n):
%o return sum(totient(d)*(n//d)**(n+1) for d in divisors(n,generator=True)) # _Chai Wah Wu_, Feb 15 2020
%Y Cf. A018804, A069097, A320940, A332517, A342432, A342433.
%K nonn
%O 1,2
%A _Ilya Gutkovskiy_, Nov 02 2018
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