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%I #7 Sep 08 2022 08:46:25
%S 1,2,10,84,1301,15693,376762,6168552,176787631,3770427352,
%T 142364319626,3152758480715,154718778284149,4340093860950619,
%U 210971170836848270,7281694486114555088,435659030617933827137,14181121059071691716406,1052864393300587929716722,41673907052879908244100770
%N a(n) = Sum_{k=1..n} (k/gcd(n, k))^n.
%F a(n) = Sum_{k=1..n} (lcm(n, k)/n)^n.
%F a(n) = Sum_{d|n} Sum_{k=1..d, gcd(k, d) = 1} k^n.
%t Table[Sum[(k/GCD[n, k])^n, {k, 1, n}], {n, 1, 20}]
%t Table[Sum[Sum[If[GCD[k, d] == 1, k^n, 0], {k, 1, d}], {d, Divisors[n]}], {n, 1, 20}]
%o (Magma) [&+[(k div Gcd(n,k))^n:k in [1..n]]:n in [1..20]]; // _Marius A. Burtea_, Feb 18 2020
%Y Cf. A031971, A057661, A226561, A332517, A332621, A332652, A332653, A332654.
%K nonn
%O 1,2
%A _Ilya Gutkovskiy_, Feb 18 2020
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