%I #16 Feb 16 2019 11:57:12
%S 7,13,21,31,43,57,1,91,7,133,157,183,2,52,273,307,343,19,18,463,3,553,
%T 601,651,703,1,37,26,931,993,4,1123,1191,1261,38,61,27,9,105,1723,
%U 1807,372,5,2071,91,2257,2353,2451,119,2653,2757,14,2971,127,3193,13,6,3541
%N Smallest k > 0 such that nk+1 is a cube.
%D Dorin Andrica, Vlad Crişan, The smallest nontrivial solution to x^k == 1 (mod n) ..., Amer. Math. Monthly 126 (2019), 173-178.
%H Robert G. Wilson v, <a href="/A076947/b076947.txt">Table of n, a(n) for n = 1..1000</a>
%t Do[k = 1; While[ !IntegerQ[(n*k + 1)^(1/3)], k++ ]; Print[k], {n, 1, 58}]
%t f[n_] := Block[{x = 2}, While[ Mod[x^3 - 1, n] != 0, x++]; (x^3 - 1)/n]; Array[f, 58] (* _Robert G. Wilson v_, Mar 29 2016 *)
%o (PARI) a(n) = my(k = 1); while(! ispower(n*k+1, 3), k++); k; \\ _Michel Marcus_, Mar 30 2016
%Y Cf. A091733, A266236.
%K nonn
%O 1,1
%A _Amarnath Murthy_, Oct 20 2002
%E Edited and extended by _Robert G. Wilson v_, Oct 21 2002