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%I #20 Mar 19 2021 07:00:59
%S 1,2,65,258,1048577,4610,78364164097,4294971394,101559956672513,
%T 1100585369602,10000000000000000000001,281474977071106,
%U 11447545997288281555215581185,6140964151415455875074,1237940039285381374411014145,79228162514264619068521709570
%N a(n) = Sum_{d|n} phi(d)^(n+d).
%H Seiichi Manyama, <a href="/A342608/b342608.txt">Table of n, a(n) for n = 1..220</a>
%F a(n) = Sum_{k=1..n} phi(n/gcd(k,n))^(n + n/gcd(k,n) - 1).
%F G.f.: Sum_{k>=1} (phi(k)^2 * x)^k/(1 - (phi(k) * x)^k).
%F If p is prime, a(p) = 1 + (p-1)^(2*p).
%t a[n_] := DivisorSum[n, EulerPhi[#]^(n + #) &]; Array[a, 20] (* _Amiram Eldar_, Mar 17 2021 *)
%o (PARI) a(n) = sumdiv(n, d, eulerphi(d)^(n+d));
%o (PARI) a(n) = sum(k=1, n, eulerphi(n/gcd(k, n))^(n+n/gcd(k, n)-1));
%o (PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, (eulerphi(k)^2*x)^k/(1-(eulerphi(k)*x)^k)))
%Y Cf. A000010, A342488, A342607, A342613.
%K nonn
%O 1,2
%A _Seiichi Manyama_, Mar 16 2021
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