A341902 Least k > 1 such that (n^3+k)/(n+k) is an integer.

2, 2, 4, 3, 2, 3, 4, 5, 4, 3, 5, 4, 10, 8, 7, 5, 4, 7, 16, 5, 8, 3, 11, 10, 6, 5, 4, 9, 8, 6, 28, 9, 12, 11, 8, 5, 6, 20, 19, 9, 12, 7, 40, 13, 11, 10, 23, 22, 8, 7, 20, 9, 16, 19, 12, 5, 4, 19, 29, 28, 58, 32, 31, 9, 6, 13, 12, 21, 24, 15, 35, 9, 70, 38, 37, 20, 8, 7, 13, 17, 10, 9, 41, 40, 18, 17, 16, 29, 28, 10, 15, 13, 32

Offset: 0

Author

Seiichi Manyama, Jun 04 2021

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A301941, A341889.

Programs

Mathematica

a[n_] := Module[{k = 2}, While[! Divisible[n^3 + k, n + k], k++]; k]; Array[a, 100, 0] (* Amiram Eldar, Jun 04 2021 *)

PARI

a(n) = my(k=2); while((n^3+k)%(n+k)!=0, k++); k;

Formula

a(n) <= n-2 for all n > 3.