A372918 a(n) = Sum_{k=1..n} gcd(k^3,n^2).

1, 5, 11, 26, 29, 55, 55, 148, 141, 145, 131, 286, 181, 275, 319, 680, 305, 705, 379, 754, 605, 655, 551, 1628, 1145, 905, 2367, 1430, 869, 1595, 991, 3408, 1441, 1525, 1595, 3666, 1405, 1895, 1991, 4292, 1721, 3025, 1891, 3406, 4089, 2755, 2255, 7480, 4501, 5725, 3355

Offset

1,2

Links

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

Formula

Multiplicative with a(p^e) = p^e * (1 + ((p-1)/p) * Sum_{i=1..2*e} p^(floor(2*i/3))). - Amiram Eldar, May 24 2024

Mathematica

a[n_] := Sum[GCD[k^3, n^2], {k, 1, n}]; Array[a, 100] (* Amiram Eldar, May 24 2024 *)

Prog

(PARI) a(n) = sum(k=1, n, gcd(k^3, n^2));

Crossrefs

Cf. A069097, A078430, A343497, A372882.

Sequence in context: A326161 A354838 A038253 * A274681 A287350 A294091

Adjacent sequences: A372915 A372916 A372917 * A372919 A372920 A372921

Keyword

nonn,mult

Author

Seiichi Manyama, May 16 2024

Status

approved