A076410 (Sum of the quadratic residues of prime(n)) / prime(n).

1, 1, 2, 3, 4, 4, 4, 7, 6, 9, 10, 10, 9, 13, 13, 15, 16, 14, 18, 17, 19, 22, 24, 25, 23, 25, 27, 28, 29, 30, 34, 33, 37, 34, 39, 40, 36, 43, 42, 45, 41, 48, 49, 45, 51, 52, 54, 57, 58, 52, 60, 59, 64, 59, 67, 62, 69, 70, 69, 73, 75, 68, 78, 79, 81, 84, 84, 87, 88, 80, 87, 93, 93

Offset: 3

Author

R. K. Guy, Oct 08 2002

Keywords

• nonn

Comments

Always an integer for primes > 3.

References

• Kenneth A. Ribet, Modular forms and Diophantine questions, Challenges for the 21st century (Singapore 2000), 162-182; World Sci. Publishing, River Edge NJ 2001; Math. Rev. 2002i:11030.

Programs

Mathematica

Table[ Apply[ Plus, Flatten[ Position[ Table[ JacobiSymbol[i, Prime[n]], {i, 1, Prime[n] - 1}], 1]]] /Prime[n], {n, 3, 50}]

Formula

a(n) = A076409(n)/prime(n).

a(n) ~= p(n)/4. - David W. Wilson, Oct 09 2002

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

Extensions

Edited and extended by Robert G. Wilson v, Oct 09 2002