

A076942


Smallest k > 0 such that nk+1 is a square.


8



3, 4, 1, 2, 3, 4, 5, 1, 7, 8, 9, 2, 11, 12, 1, 3, 15, 16, 17, 4, 3, 20, 21, 1, 23, 24, 25, 6, 27, 4, 29, 7, 3, 32, 1, 8, 35, 36, 5, 2, 39, 4, 41, 10, 8, 44, 45, 1, 47, 48, 5, 12, 51, 52, 8, 3, 7, 56, 57, 2, 59, 60, 1, 15, 3, 8, 65, 16, 7, 12, 69, 4, 71, 72, 9, 18, 15, 8, 77, 1, 79, 80, 81
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OFFSET

1,1


COMMENTS

a(n) <= n2 for n > 2; a(p) = p2 if p is a prime > 2. [Comment corrected by Floris van Doorn, Jan 31 2009]
a(n) = n  2 precisely when n > 2 has a primitive root; that is, for 4, and p^k and 2*p^k for p an odd prime and k > 0. [From Franklin T. AdamsWatters, Apr 13 2009]


REFERENCES

Dorin Andrica, Vlad Crişan, The smallest nontrivial solution to x^k == 1 (mod n) ..., Amer. Math. Monthly 126 (2019), 173178.


LINKS



FORMULA



MATHEMATICA

Do[k = 1; While[ !IntegerQ[Sqrt[n*k + 1]], k++ ]; Print[k], {n, 1, 85}]


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



