A280302 - OEIS

A280302

Smallest k such that (n+1)^k - n^k is divisible by a square > 1.

6, 10, 4, 2, 21, 20, 3, 20, 33, 6, 20, 2, 2, 5, 21, 6, 10, 6, 6, 4, 4, 2, 7, 2, 6, 3, 10, 4, 18, 6, 2, 10, 20, 6, 57, 17, 2, 14, 42, 2, 10, 10, 6, 39, 14, 4, 10, 20, 2, 21, 20, 6, 4, 21, 6, 20, 10, 2, 5, 2, 5, 2, 20, 6, 42, 14, 2, 6, 55, 6, 3, 7, 2, 42, 3, 2

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OFFSET

1,1

COMMENTS

a(209) > 70.

a(n) <= p^2 - p, where p = A053670(n). - Jinyuan Wang, May 15 2020

LINKS

Lars Blomberg, Table of n, a(n) for n = 1..208

EXAMPLE

a(1) = 6 is because (1+1)^6 - 1^6 = 63 is divisible by 9 = 3^2.

PROG

(PARI) a(n) = {my(k = 1); while (issquarefree((n+1)^k - n^k), k++); k; } \\ Michel Marcus, Jan 14 2017