A076942 - OEIS

%I #13 Feb 16 2019 11:56:40

%S 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,

%T 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,

%U 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

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

%C a(n) <= n-2 for n > 2; a(p) = p-2 if p is a prime > 2. [Comment corrected by Floris van Doorn, Jan 31 2009]

%C 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. Adams-Watters_, Apr 13 2009]

%D Dorin Andrica, Vlad Crişan, The smallest nontrivial solution to x^k == 1 (mod n) ..., Amer. Math. Monthly 126 (2019), 173-178.

%H Floris P. van Doorn, <a href="/A076942/b076942.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = ((A215653(n))^2-1)/n.

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

%Y Cf. A033948, A033949, A215653. [From _Franklin T. Adams-Watters_, Apr 13 2009]

%K nonn

%O 1,1

%A _Amarnath Murthy_, Oct 19 2002

%E Edited and extended by _Robert G. Wilson v_, Oct 21 2002