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%I #12 Sep 08 2022 08:46:25
%S 1,2,6,12,31,33,92,96,165,172,386,239,651,499,656,776,1497,846,2110,
%T 1262,1903,2037,3796,1867,4181,3408,4530,3673,7715,3183,9456,6232,
%U 7761,7754,10062,6248,16207,10889,12980,9906,22141,9308,25586,15027,17075,19483,33512,14851
%N a(n) = Sum_{k=1..n} (k/gcd(n, k))^2.
%C Inverse Moebius transform of A053818.
%H Seiichi Manyama, <a href="/A332654/b332654.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = Sum_{k=1..n} (lcm(n, k)/n)^2.
%F a(n) = Sum_{d|n} Sum_{k=1..d, gcd(k, d) = 1} k^2.
%t Table[Sum[(k/GCD[n, k])^2, {k, 1, n}], {n, 1, 48}]
%t Table[Sum[Sum[If[GCD[k, d] == 1, k^2, 0], {k, 1, d}], {d, Divisors[n]}], {n, 1, 48}]
%o (Magma) [&+[(k div Gcd(n,k))^2:k in [1..n]]:n in [1..50]]; // _Marius A. Burtea_, Feb 18 2020
%Y Cf. A053818, A057661, A068963, A069097, A320941, A332655.
%K nonn
%O 1,2
%A _Ilya Gutkovskiy_, Feb 18 2020
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