cp's OEIS Frontend

A331388 a(n) = Sum_{k=1..n} mu(gcd(n, k)) * k / gcd(n, k).

%I A331388 #24 Sep 08 2022 08:46:25
%S A331388 1,0,2,3,9,3,20,12,24,10,54,15,77,21,48,48,135,24,170,57,103,55,252,
%T A331388 60,240,78,216,123,405,47,464,192,273,136,390,144,665,171,388,228,819,
%U A331388 102,902,327,456,253,1080,240,1008,240,678,465,1377,216,1036,492,853,406,1710
%N A331388 a(n) = Sum_{k=1..n} mu(gcd(n, k)) * k / gcd(n, k).
%C A331388 Moebius transform of A023896.
%F A331388 a(n) = (1/n) * Sum_{k=1..n} mu(gcd(n, k)) * lcm(n, k).
%F A331388 a(n) = Sum_{d|n} mu(n/d) * A023896(d).
%F A331388 a(n) = Sum_{d|n} A007427(n/d) * A057661(d).
%F A331388 Sum_{k=1..n} a(k) ~ n^3 / (Pi^2 * Zeta(3)). - _Vaclav Kotesovec_, Feb 19 2020
%t A331388 Table[Sum[MoebiusMu[GCD[n, k]] k/GCD[n, k], {k, 1, n}], {n, 1, 65}]
%t A331388 A023896[n_] := Sum[If[GCD[n, k] == 1, k, 0], {k, 1, n}]; Table[Sum[MoebiusMu[n/d] A023896[d], {d, Divisors[n]}], {n, 1, 65}]
%o A331388 (Magma) [&+[MoebiusMu(Gcd(n,k))*(k div Gcd(n,k)):k in [1..n]]:n in [1..60]]; // _Marius A. Burtea_, Feb 18 2020
%Y A331388 Cf. A007427, A007431, A008683, A023896, A057661, A063445.
%K A331388 nonn
%O A331388 1,3
%A A331388 _Ilya Gutkovskiy_, Feb 18 2020