A125613 Sum of the squares of the quadratic residues of prime(n).

1, 1, 17, 21, 132, 351, 816, 874, 1104, 4031, 3286, 8473, 11726, 11868, 11233, 24857, 28143, 38247, 46766, 40754, 66722, 65017, 83249, 120150, 156364, 173013, 152955, 184147, 218763, 245436, 297053, 327500, 437030, 413803, 556217, 488334, 652335

Offset

1,3

Comments

For all n > 3, 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

Example

The quadratic residues of 7=prime(4) are 1, 2 and 4. Hence a(4)=1^2 + 2^2 + 4^2=21.

Mathematica

Table[Total[ResourceFunction["QuadraticResidues"][Prime[n]]^2], {n, 37}] (* James C. McMahon, Dec 19 2024 *)

Prog

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

Crossrefs

Cf. A076409, A076410, A125613-A125618.

Sequence in context: A138600 A050845 A219396 * A147052 A147132 A146840

Adjacent sequences: A125610 A125611 A125612 * A125614 A125615 A125616

Keyword

easy,nonn

Author

Nick Hobson, Nov 30 2006

Status

approved