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%I #15 Mar 18 2021 08:25:22
%S 1,2,9,18,1025,98,279937,65666,10077825,1310722,100000000001,16780802,
%T 106993205379073,91424858114,35184439199745,281476050460674,
%U 295147905179352825857,118486616186882,708235345355337676357633,1152921796664688642,46005120518729441509377,11000000000000000000002
%N a(n) = Sum_{d|n} phi(n/d)^(n-d+1).
%H Seiichi Manyama, <a href="/A342619/b342619.txt">Table of n, a(n) for n = 1..388</a>
%F a(n) = Sum_{k=1..n} phi(n/gcd(k,n))^(n - gcd(k,n)).
%F G.f.: Sum_{k>=1} (phi(k) * x)^k/(1 - phi(k)^(k-1) * x^k).
%F If p is prime, a(p) = 1 + (p-1)^p.
%t a[n_] := DivisorSum[n, EulerPhi[n/#]^(n - # + 1) &]; Array[a, 20] (* _Amiram Eldar_, Mar 17 2021 *)
%o (PARI) a(n) = sumdiv(n, d, eulerphi(n/d)^(n-d+1));
%o (PARI) a(n) = sum(k=1, n, eulerphi(n/gcd(k, n))^(n-gcd(k, n)));
%o (PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, (eulerphi(k)*x)^k/(1-eulerphi(k)^(k-1)*x^k)))
%Y Cf. A000010, A342612.
%K nonn
%O 1,2
%A _Seiichi Manyama_, Mar 16 2021
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