A125617 Sum of the squares of the quadratic nonresidues of prime(n).

0, 4, 13, 70, 253, 299, 680, 1235, 2691, 3683, 6169, 7733, 10414, 13717, 22278, 23373, 38586, 35563, 51255, 76041, 60298, 96222, 103916, 110894, 143172, 165337, 206000, 218494, 206991, 229164, 377698, 413305, 410726, 471766, 535357, 647941, 625331

Offset: 1

Author

Nick Hobson, Nov 30 2006

Keywords

• easy
• nonn

Comments

For all n > 3, prime(n) divides a(n).

Examples

			The quadratic nonresidues of 7=prime(4) are 3, 5 and 6. Hence a(4) = 3^2 + 5^2 + 6^2 = 70.
		

References

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

Links

• Nick Hobson, Table of n, a(n) for n = 1..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,Prime@Range[37]}] (* James C. McMahon, Dec 19 2024 *)

PARI

vector(37, n, p=prime(n); t=1; for(i=2, (p-1)/2, t+=((i^2)%p)^2); p*(p-1)*(2*p-1)/6-t)