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

1, 1, 8, 14, 49, 26, 146, 112, 234, 149, 604, 238, 1013, 440, 842, 896, 2311, 702, 3248, 1386, 2491, 1814, 5818, 1904, 6200, 3041, 6318, 4102, 11773, 2524, 14414, 7168, 10277, 6935, 14504, 6552, 24641, 9746, 17230, 11088, 33619, 7471, 38828, 16926, 23166, 17456

Offset: 1

Author

Ilya Gutkovskiy, Feb 18 2020

Keywords

• nonn

Crossrefs

Cf. A007427, A008683, A056789, A063445, A331388.

Programs

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

Mathematica

Table[Sum[MoebiusMu[GCD[n, k]] LCM[n, k]/GCD[n, k], {k, 1, n}], {n, 1, 46}]
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}]

PARI

a(n) = sum(k=1, n, moebius(gcd(n, k))*lcm(n, k)/gcd(n, k)); \\ Michel Marcus, Feb 18 2020

Formula

a(n) = Sum_{d|n} A007427(n/d) * A056789(d).