A242441 - OEIS

%I #14 May 14 2014 14:34:00

%S 1,2,3,4,5,6,8,10,12,15,16,18,20,21,24,28,30,32,39,40,48,50,56,60,63,

%T 70,72,80,88,102,110,112,120,126,156,168,204,213,220,232,240,252,272,

%U 273,280,312,372,378,408,520,527,546,760,765,780,813,840,968,1320,1715,1848

%N Numbers n such that there are no integer k < sqrt(n) and prime p < n with k^2*p == 1 (mod n).

%C Conjecture: The sequence only has 61 terms as listed.

%C We have checked this extension of the conjecture in A242425 for n up to 10^7.

%H Zhi-Wei Sun, <a href="/A242441/b242441.txt">Table of n, a(n) for n = 1..61</a>

%e a(5) = 5 since none of 1^2*2 = 2, 1^2*3 = 3, 2^2*2 = 8 and 2^2*3 = 12 is congruent to 1 modulo 5.

%t r[k_,n_]:=r[k,n]=PowerMod[k^2,-1,n]

%t m=0;Do[Do[If[GCD[k,n]==1&&PrimeQ[r[k,n]],Goto[aa]],{k,1,Sqrt[n-1]}];m=m+1;Print[m," ",n];Label[aa];Continue,{n,1,2000}]

%Y Cf. A000040, A000290, A242425, A242444.

%K nonn

%O 1,2

%A _Zhi-Wei Sun_, May 14 2014