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%I #8 Sep 08 2022 08:46:25
%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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