A332654 a(n) = Sum_{k=1..n} (k/gcd(n, k))^2.

1, 2, 6, 12, 31, 33, 92, 96, 165, 172, 386, 239, 651, 499, 656, 776, 1497, 846, 2110, 1262, 1903, 2037, 3796, 1867, 4181, 3408, 4530, 3673, 7715, 3183, 9456, 6232, 7761, 7754, 10062, 6248, 16207, 10889, 12980, 9906, 22141, 9308, 25586, 15027, 17075, 19483, 33512, 14851

Offset: 1

Author

Ilya Gutkovskiy, Feb 18 2020

Keywords

• nonn

Comments

Inverse Moebius transform of A053818.

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A053818, A057661, A068963, A069097, A320941, A332655.

Programs

Magma

[&+[(k div Gcd(n,k))^2:k in [1..n]]:n in [1..50]]; // Marius A. Burtea, Feb 18 2020

Mathematica

Table[Sum[(k/GCD[n, k])^2, {k, 1, n}], {n, 1, 48}]
Table[Sum[Sum[If[GCD[k, d] == 1, k^2, 0], {k, 1, d}], {d, Divisors[n]}], {n, 1, 48}]

Formula

a(n) = Sum_{k=1..n} (lcm(n, k)/n)^2.

a(n) = Sum_{d|n} Sum_{k=1..d, gcd(k, d) = 1} k^2.