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 A332653 a(n) = (1/n) * Sum_{k=1..n} n^(k/gcd(n, k)). 2

%I

%S 1,2,5,19,157,1306,19609,266372,5321721,101001214,2593742461,

%T 61920391842,1941507093541,56984643437138,2076518238897649,

%U 72340172854919941,3041324492229179281,121440691499123469858,5784852794328402307381,262799364106291328009626

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

%F a(n) = (1/n) * Sum_{k=1..n} n^(lcm(n, k)/n).

%F a(n) = Sum_{d|n} Sum_{k=1..d, gcd(k, d) = 1} n^(k-1).

%F a(n) = A332652(n) / n.

%t Table[(1/n) Sum[n^(k/GCD[n, k]), {k, 1, n}], {n, 1, 20}]

%t Table[Sum[Sum[If[GCD[k, d] == 1, n^(k - 1), 0], {k, 1, d}], {d, Divisors[n]}], {n, 1, 20}]

%o (MAGMA) [(1/n)*&+[n^(k div Gcd(n,k)):k in [1..n]]:n in [1..21]]; // _Marius A. Burtea_, Feb 18 2020

%Y Cf. A023037, A056665, A057661, A226561, A228640, A332620, A332621, A332652, A332655.

%K nonn

%O 1,2

%A _Ilya Gutkovskiy_, Feb 18 2020

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Last modified April 20 17:56 EDT 2021. Contains 343135 sequences. (Running on oeis4.)