cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A332658 a(n) = Sum_{k=1..n} mu(gcd(n, k)) * lcm(n, k) / gcd(n, k).

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%I A332658 #9 Sep 08 2022 08:46:25
%S A332658 1,1,8,14,49,26,146,112,234,149,604,238,1013,440,842,896,2311,702,
%T A332658 3248,1386,2491,1814,5818,1904,6200,3041,6318,4102,11773,2524,14414,
%U A332658 7168,10277,6935,14504,6552,24641,9746,17230,11088,33619,7471,38828,16926,23166,17456
%N A332658 a(n) = Sum_{k=1..n} mu(gcd(n, k)) * lcm(n, k) / gcd(n, k).
%F A332658 a(n) = Sum_{d|n} A007427(n/d) * A056789(d).
%t A332658 Table[Sum[MoebiusMu[GCD[n, k]] LCM[n, k]/GCD[n, k], {k, 1, n}], {n, 1, 46}]
%t A332658 A007427[n_] := Sum[MoebiusMu[n/d] MoebiusMu[d], {d, Divisors[n]}]; A056789[n_] := Sum[LCM[n, k]/GCD[n, k], {k, 1, n}]; Table[Sum[A007427[n/d] A056789[d], {d, Divisors[n]}], {n, 1, 46}]
%o A332658 (Magma) [&+[MoebiusMu(Gcd(n,k))*Lcm(n,k)/ Gcd(n,k):k in [1..n]]:n in [1..50]]; // _Marius A. Burtea_, Feb 18 2020
%o A332658 (PARI) a(n) = sum(k=1, n, moebius(gcd(n, k))*lcm(n, k)/gcd(n, k)); \\ _Michel Marcus_, Feb 18 2020
%Y A332658 Cf. A007427, A008683, A056789, A063445, A331388.
%K A332658 nonn
%O A332658 1,3
%A A332658 _Ilya Gutkovskiy_, Feb 18 2020