A125614 (Sum of the squares of the quadratic residues of prime(n)) / prime(n).

3, 12, 27, 48, 46, 48, 139, 106, 229, 286, 276, 239, 469, 477, 627, 698, 574, 914, 823, 1003, 1350, 1612, 1713, 1485, 1721, 2007, 2172, 2339, 2500, 3190, 2977, 3733, 3234, 4155, 4306, 3688, 5023, 4848, 5529, 4791, 6356, 6517, 5655, 7051, 7452, 7964, 8845

Offset: 4

Author

Nick Hobson, Nov 30 2006

Keywords

• easy
• nonn

Comments

Always an integer for primes > 5.

Examples

			The quadratic residues of 7=prime(4) are 1, 2 and 4. Hence a(4) = (1^2 + 2^2 + 4^2)/7 = 3.
		

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..1003

Crossrefs

Cf. A076409, A076410, A125613-A125618.

Programs

Mathematica

Table[Total[ResourceFunction["QuadraticResidues"][Prime[n]]^2/Prime[n]], {n,4, 50}] (* James C. McMahon, Dec 19 2024 *)

PARI

vector(47, m, p=prime(m+3); t=1; for(i=2, (p-1)/2, t+=((i^2)%p)^2); t/p)

Formula

a(n) = A125613(n)/prime(n).