A125616 - OEIS

%I #20 Feb 13 2024 11:33:49

%S 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 27,28,34,35,34,36,37,41,39,41,47,43,47,45,54,48,49,54,54,59,59,57,58,

%U 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 (Sum of the quadratic nonresidues of prime(n)) / prime(n).

%C Always an integer for primes >= 5.

%D D. M. Burton, Elementary Number Theory, McGraw-Hill, Sixth Edition (2007), p. 185.

%H Nick Hobson, <a href="/A125616/b125616.txt">Table of n, a(n) for n = 3..1000</a>

%F a(n) = A125615(n)/prime(n).

%F If prime(n) = 4k+1 then a(n) = k = A076410(n).

%e The quadratic nonresidues of 7=prime(4) are 3, 5 and 6. Hence a(4) = (3+5+6)/7 = 2.

%p a:= proc(n) local p;

%p    p:= ithprime(n);

%p    convert(select(t->numtheory:-legendre(t,p)=-1, [$1..p-1]),`+`)/p;

%p end proc:

%p seq(a(n),n=3..100); # _Robert Israel_, May 10 2015

%t Table[Total[Flatten[Position[Table[JacobiSymbol[a, p], {a, p - 1}], -1]]]/ p, {p, Prime[Range[3, 100]]}] (* _Geoffrey Critzer_, May 10 2015 *)

%o (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 Cf. A002143, A076409, A076410, A125613-A125618.

%K easy,nonn

%O 3,2

%A _Nick Hobson_, Nov 30 2006