A125618 (Sum of the squares of the quadratic nonresidues of prime(n)) / prime(n).

10, 23, 23, 40, 65, 117, 127, 199, 209, 254, 319, 474, 441, 654, 583, 765, 1071, 826, 1218, 1252, 1246, 1476, 1637, 2000, 2042, 1899, 2028, 2974, 3155, 2998, 3394, 3593, 4291, 3983, 4469, 5525, 4867, 5743, 5301, 7274, 5964, 6321, 7446, 7684, 9013, 9099

Offset: 4

Author

Nick Hobson, Nov 30 2006

Keywords

• easy
• nonn

Comments

Always an integer for primes > 5.

Examples

			The quadratic nonresidues of 7=prime(4) are 3, 5 and 6. Hence a(4) = (3^2 + 5^2 + 6^2)/7 = 10.
		

References

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

Links

• Nick Hobson, Table of n, a(n) for n = 4..1000

Crossrefs

Cf. A076409, A076410, A125613-A125618.

Programs

Mathematica

Table[Total[Complement[Range[p-1], Union[Table[PowerMod[k, 2, p], {k, p}]]]^2]/p, {p, Prime@Range[4,49]}] (* James C. McMahon, Dec 20 2024 *)

PARI

vector(46, m, p=prime(m+3); t=1; for(i=2, (p-1)/2, t+=((i^2)%p)^2); (p-1)*(2*p-1)/6-t/p)

Formula

a(n) = A125617(n)/prime(n).