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

Offset: 1

Author

Juri-Stepan Gerasimov, Dec 31 2016

Keywords

• nonn

Comments

a(209) > 70.

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

Examples

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

Links

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

Crossrefs

Cf. A049094, A053670, A237043, A280203, A280208, A280209, A280296, A282176, A282177, A280307.

Cf. A289629, A280547, A289985.

Programs

PARI

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

Extensions

More terms from Lars Blomberg, Jan 10 2017