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A125616 (Sum of the quadratic nonresidues of prime(n)) / prime(n).

%I A125616 #20 Feb 13 2024 11:33:49
%S A125616 1,2,3,3,4,5,7,7,9,9,10,11,14,13,16,15,17,21,18,22,22,22,24,25,28,28,
%T A125616 27,28,34,35,34,36,37,41,39,41,47,43,47,45,54,48,49,54,54,59,59,57,58,
%U A125616 67,60,66,64,72,67,73,69,70,72,73,78,87,78,79,84,84,89,87,88,99,96,93,96
%N A125616 (Sum of the quadratic nonresidues of prime(n)) / prime(n).
%C A125616 Always an integer for primes >= 5.
%D A125616 D. M. Burton, Elementary Number Theory, McGraw-Hill, Sixth Edition (2007), p. 185.
%H A125616 Nick Hobson, <a href="/A125616/b125616.txt">Table of n, a(n) for n = 3..1000</a>
%F A125616 a(n) = A125615(n)/prime(n).
%F A125616 If prime(n) = 4k+1 then a(n) = k = A076410(n).
%e A125616 The quadratic nonresidues of 7=prime(4) are 3, 5 and 6. Hence a(4) = (3+5+6)/7 = 2.
%p A125616 a:= proc(n) local p;
%p A125616    p:= ithprime(n);
%p A125616    convert(select(t->numtheory:-legendre(t,p)=-1, [$1..p-1]),`+`)/p;
%p A125616 end proc:
%p A125616 seq(a(n),n=3..100); # _Robert Israel_, May 10 2015
%t A125616 Table[Total[Flatten[Position[Table[JacobiSymbol[a, p], {a, p - 1}], -1]]]/ p, {p, Prime[Range[3, 100]]}] (* _Geoffrey Critzer_, May 10 2015 *)
%o A125616 (PARI) vector(73, m, p=prime(m+2); t=1; for(i=2, (p-1)/2, t+=((i^2)%p)); (p-1)/2-t/p)
%Y A125616 Cf. A002143, A076409, A076410, A125613-A125618.
%K A125616 easy,nonn
%O A125616 3,2
%A A125616 _Nick Hobson_, Nov 30 2006