%I #25 Jul 26 2019 18:29:24
%S 1,2,3,4,5,6,7,8,9,10,12,13,15,16,18,19,21,22,24,25,27,28,30,33,37,40,
%T 42,43,45,48,57,58,60,63,67,70,72,78,85,88,93,100,102,105,112,120,130,
%U 133,135,147,148,163,165,168,177,190,210,232,240,247,253,267,268,273,280,312,330,333,345,357,385,408,462,520,522,652,708,760,840,928,1320,1365,1467,1848
%N Numbers n such that n is a quadratic nonresidue modulo all odd primes p <= sqrt(n) which do not divide n.
%C Contains A000926 and A003173 (except the term 11) as subsequences.
%C Conjecture: 1848 is the last term of this sequence.
%e 42 is in this sequence because sqrt(42) = 6.480740..., and 42 is quadratic nonresidue mod all odd primes < 6.480740... not dividing 42 (only mod 5).
%e 67 is in this sequence because sqrt(67) = 8.185352..., and 67 is quadratic nonresidue mod all odd primes < 8.185352... not dividing 67 (mod 3, mod 5 and mod 7).
%e 17 is not in this sequence because 17 is quadratic residue mod 3 and 3 < sqrt(17) and 3 does not divide 17.
%e 90 is not in this sequence because 90 is quadratic residue mod 7 and 7 < sqrt(90) and 7 does not divide 90.
%e For n < 9, the range of p is empty, thus the numbers n < 9 are trivially in this sequence.
%o (PARI) a(n)=forprime(p=3, ,if(kronecker(n,p)==1,return(p)))
%o for(k=1, 10^6,if(a(k)>sqrt(k),print1(k, ", ")))
%Y Cf. A000926, A003173.
%K nonn
%O 1,2
%A _Richard N. Smith_, Jul 13 2019
