A125615 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

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

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.

FORMULA

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

EXAMPLE

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

PROG

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

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.

Sequence in context: A336229 A296502 A036681 * A096772 A090803 A018015

Adjacent sequences: A125612 A125613 A125614 * A125616 A125617 A125618

KEYWORD

easy,nonn

AUTHOR

Nick Hobson, Nov 30 2006

STATUS

approved