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

2,1

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.

Links

Table of n, a(n) for n=2..79.

Prog

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

Crossrefs

Cf. A013929, A334213, A334214.

Sequence in context: A099550 A349341 A099549 * A082725 A308655 A356365

Adjacent sequences: A334209 A334210 A334211 * A334213 A334214 A334215

Keyword

nonn

Author

Gionata Neri, Apr 18 2020

Status

approved