A372882 a(n) = Sum_{k=1..n} gcd(k^3,n).

1, 3, 5, 10, 9, 15, 13, 36, 33, 27, 21, 50, 25, 39, 45, 104, 33, 99, 37, 90, 65, 63, 45, 180, 145, 75, 261, 130, 57, 135, 61, 336, 105, 99, 117, 330, 73, 111, 125, 324, 81, 195, 85, 210, 297, 135, 93, 520, 385, 435, 165, 250, 105, 783, 189, 468, 185, 171, 117, 450

Offset

1,2

Links

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

László Tóth, Menon's identity and arithmetical sums representing functions of several variables, Rend. Sem. Mat. Univ. Politec. Torino, Vol. 69, No. 1 (2011), pp. 97-110.

Formula

From Amiram Eldar, May 24 2024: (Start)

a(n) = n * Sum_{d|n} A000010(d)*A000189(d)/d (Tóth, 2011).

Multiplicative with a(p^e) = p^e * (1 + ((p-1)/p) * Sum_{i=1..e} p^(floor(2*i/3))). (End)

Mathematica

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

Prog

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

Crossrefs

Cf. A018804, A078430.

Cf. A000010, A000189.

Sequence in context: A176629 A069193 A078430 * A345892 A373210 A342424

Adjacent sequences: A372879 A372880 A372881 * A372883 A372884 A372885

Keyword

nonn,mult

Author

Seiichi Manyama, May 15 2024

Status

approved