A334212 - OEIS

%I #16 Jun 04 2020 13:11:37

%S 3,1,5,3,7,1,1,5,11,1,10,7,3,1,17,1,2,1,3,11,10,1,1,13,1,1,10,3,31,1,

%T 2,10,5,1,37,10,2,1,5,2,10,1,1,21,47,1,1,1,3,1,10,1,5,1,3,2,10,1,14,

%U 21,1,1,5,3,21,1,2,3,2,1,10,10,1,1,7,3,10,1

%N Least number k such that n^k + 1 is not squarefree.

%C For n == 1 (mod 4) (n not 1), a(n) <= (n + 1)/2.

%C For n == 3 (mod 4), a(n) = 1.

%C For even n, a(n) <= n + 1.

%C Existence proof for n >= 2 and upper bounds use the binomial formula.

%o (PARI) for(n=2,79, for(k=1,n+1, !issquarefree(n^k+1)&!print1(k", ")&break))

%Y Cf. A013929, A334213, A334214.

%K nonn

%O 2,1

%A _Gionata Neri_, Apr 18 2020