%I #27 Dec 07 2021 10:59:55

%S 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,

%T 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,

%U 20,10,2,5,2,5,2,20,6,42,14,2,6,55,6,3,7,2,42,3,2

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

%C a(209) > 70.

%C a(n) <= p^2 - p, where p = A053670(n). - _Jinyuan Wang_, May 15 2020

%H Lars Blomberg, <a href="/A280302/b280302.txt">Table of n, a(n) for n = 1..208</a>

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

%o (PARI) a(n) = {my(k = 1); while (issquarefree((n+1)^k - n^k), k++); k;} \\ _Michel Marcus_, Jan 14 2017

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

%Y Cf. A289629, A280547, A289985.

%K nonn

%O 1,1

%A _Juri-Stepan Gerasimov_, Dec 31 2016

%E More terms from _Lars Blomberg_, Jan 10 2017