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%I #17 May 09 2021 08:07:47
%S 1,3,19,137,2501,16071,705895,8421505,258293449,4007813013,
%T 259374246011,2972767821815,279577021469773,4762869973595499,
%U 233543432626753439,9223512776490647553,778579070010669895697,13115569455375954492093,1874292305362402347591139
%N a(n) = Sum_{d|n} phi(d^n), where phi() is the Euler totient function (A000010).
%H Seiichi Manyama, <a href="/A321349/b321349.txt">Table of n, a(n) for n = 1..386</a>
%F G.f.: Sum_{k>=1} k^(k-1)*phi(k)*x^k/(1 - (k*x)^k).
%F a(n) = Sum_{d|n} d^(n-1)*phi(d).
%F a(n) = Sum_{k=1..n} (n/gcd(n,k))^(n-1).
%F From _Richard L. Ollerton_, May 08 2021: (Start)
%F a(n) = Sum_{k=1..n} phi(gcd(n,k)^n)/phi(n/gcd(n,k)).
%F a(n) = Sum_{k=1..n} gcd(n,k)^(n-1)*phi(gcd(n,k))/phi(n/gcd(n,k)). (End)
%t Table[Sum[EulerPhi[d^n], {d, Divisors[n]}], {n, 19}]
%t nmax = 19; Rest[CoefficientList[Series[Sum[k^(k - 1) EulerPhi[k] x^k/(1 - (k x)^k), {k, 1, nmax}], {x, 0, nmax}], x]]
%t Table[Sum[(n/GCD[n, k])^(n - 1), {k, n}], {n, 19}]
%o (PARI) a(n) = sumdiv(n, d, eulerphi(d^n)); \\ _Michel Marcus_, Nov 06 2018
%Y Cf. A000010, A057660, A068963, A068970, A226459, A226561.
%K nonn
%O 1,2
%A _Ilya Gutkovskiy_, Nov 06 2018
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