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a(n) = Sum_{k=1..n, gcd(n,k) = 1} k^n.
3

%I #15 Mar 28 2024 21:56:32

%S 1,1,9,82,1300,15626,376761,6161988,176787117,3769318700,142364319625,

%T 3152513804548,154718778284148,4340009120036086,210971169748692000,

%U 7281661100510001416,435659030617933827136,14181101408561469791694,1052864393300587929716721,41673894815421072916530408

%N a(n) = Sum_{k=1..n, gcd(n,k) = 1} k^n.

%H Seiichi Manyama, <a href="/A308481/b308481.txt">Table of n, a(n) for n = 1..386</a>

%t a[n_] := Sum[If[GCD[n, k] == 1, k^n, 0], {k, 1, n}]; Table[a[n], {n, 1, 20}]

%o (PARI) a(n) = sum(k=1, n, (gcd(n,k)==1)*k^n) \\ _Felix Fröhlich_, May 30 2019

%Y First superdiagonal of A308477.

%Y Cf. A031971.

%K nonn

%O 1,3

%A _Ilya Gutkovskiy_, May 30 2019