A334212 Least number k such that n^k + 1 is not squarefree.

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

Offset: 2

Author

Gionata Neri, Apr 18 2020

Keywords

• nonn

Comments

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

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

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

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

Crossrefs

Cf. A013929, A334213, A334214.

Programs

PARI

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