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A334212 Least number k such that n^k + 1 is not squarefree. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A127418 A099550 A099549 * A082725 A308655 A217663

Adjacent sequences:  A334209 A334210 A334211 * A334213 A334214 A334215

KEYWORD

nonn

AUTHOR

Gionata Neri, Apr 18 2020

STATUS

approved

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Last modified October 24 05:38 EDT 2021. Contains 348217 sequences. (Running on oeis4.)