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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
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.
PROG
(PARI) for(n=2, 79, for(k=1, n+1, !issquarefree(n^k+1)&!print1(k", ")&break))
CROSSREFS
KEYWORD
nonn
AUTHOR
Gionata Neri, Apr 18 2020
STATUS
approved