A379470 For n >= 1, a(n) = Sum_{i = 0..(n - 1)} n / GCD(n, i!).

1, 4, 9, 12, 25, 18, 49, 28, 39, 40, 121, 40, 169, 70, 65, 62, 289, 66, 361, 80, 105, 154, 529, 84, 165, 208, 135, 126, 841, 110, 961, 132, 209, 340, 217, 132, 1369, 418, 273, 160, 1681, 168, 1849, 242, 207, 598, 2209, 174, 427, 240, 425, 312, 2809, 216, 385, 238

Offset

1,2

Comments

For n >= 1, 1 <= a(n) <= n^2.

Links

Michel Marcus, Table of n, a(n) for n = 1..10000

Formula

For p prime number (A000040), a(p) = p^2.

Example

n = 3: 3/GCD(3,0!) + 3/GCD(3,1!) + 3/GCD(3,2!) = 9.

Mathematica

a[n_] := Sum[n / GCD[n, i!], {i, 0, n-1}]; Array[a, 60] (* Amiram Eldar, Dec 23 2024 *)

Prog

(PARI) a(n) = sum(i=0, n-1, n/gcd(n, i!)); \\ Michel Marcus, Aug 04 2025

Crossrefs

Cf. A000040, A000142, A057660.

Sequence in context: A197624 A339594 A199973 * A320925 A212875 A069082

Adjacent sequences: A379467 A379468 A379469 * A379471 A379472 A379473

Keyword

nonn

Author

Ctibor O. Zizka, Dec 23 2024

Status

approved