A125615 Sum of the quadratic nonresidues of prime(n).

0, 2, 5, 14, 33, 39, 68, 95, 161, 203, 279, 333, 410, 473, 658, 689, 944, 915, 1139, 1491, 1314, 1738, 1826, 1958, 2328, 2525, 2884, 2996, 2943, 3164, 4318, 4585, 4658, 5004, 5513, 6191, 6123, 6683, 7849, 7439, 8413, 8145, 10314, 9264, 9653, 10746, 11394

Offset: 1

Author

Nick Hobson, Nov 30 2006

Keywords

• easy
• nonn

Comments

For all n > 2, prime(n) divides a(n).

Examples

			The quadratic nonresidues of 7=prime(4) are 3, 5 and 6. Hence a(4) = 3+5+6 = 14.
		

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
• Christian Aebi and Grant Cairns. Sums of Quadratic residues and nonresidues, arXiv preprint arXiv:1512.00896 [math.NT], 2015.

Crossrefs

Cf. A076409, A076410, A125613-A125618.

Sums of residues, nonresidues, and their differences, for p == 1 (mod 4), p == 3 (mod 4), and all p: A171555; A282035, A282036, A282037; A076409, A125615, A282038.

Programs

Mathematica

Table[p=Prime[n];Total[Complement[Range[p-1],Union[Table[PowerMod[k, 2, p], {k, p}]]]],{n,47}] (* James C. McMahon, Dec 19 2024 *)

PARI

vector(47, n, p=prime(n); t=1; for(i=2, (p-1)/2, t+=((i^2)%p)); p*(p-1)/2-t)

Formula

If prime(n) = 4k+1 then a(n) = k(4k+1) = A076409(n).