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A076409 Sum of the quadratic residues of prime(n). 16
1, 1, 5, 7, 22, 39, 68, 76, 92, 203, 186, 333, 410, 430, 423, 689, 767, 915, 1072, 994, 1314, 1343, 1577, 1958, 2328, 2525, 2369, 2675, 2943, 3164, 3683, 3930, 4658, 4587, 5513, 5134, 6123, 6520, 6012, 7439, 7518, 8145, 7831, 9264, 9653, 8955, 10761, 11596 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Row sums of A063987. - R. J. Mathar, Jan 08 2015

REFERENCES

Aebi, Christian, and Grant Cairns. "Sums of Quadratic residues and nonresidues." arXiv preprint arXiv:1512.00896 (2015).

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.

LINKS

Moshe Levin, Table of n, a(n) for n = 1..1000

FORMULA

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

MAPLE

A076409 := proc(n)

  local a, p, i ;

  p := ithprime(n) ;

  a := 0 ;

  for i from 1 to p-1 do

    if numtheory[legendre](i, p) = 1 then

       a := a+i ;

    end if;

  end do;

  a ;

end proc: # R. J. Mathar, Feb 26 2011

MATHEMATICA

Join[{1, 1}, Table[ Apply[ Plus, Flatten[ Position[ Table[ JacobiSymbol[i, Prime[n]], {i, 1, Prime[n] - 1}], 1]]], {n, 3, 48}]]

Join[{1}, Table[p=Prime[n]; If[Mod[p, 4]==1, p(p-1)/4, Sum[PowerMod[k, 2, p], {k, p/2}]], {n, 2, 1000}]] (* Moshe Levin, Nov 02 2011 *)

PROG

(PARI) a(n, p=prime(n))=if(p<5, return(1)); if(k%4==1, return(p\4*p)); sum(k=1, p-1, k^2%p) \\ Charles R Greathouse IV, Feb 21 2017

CROSSREFS

Cf. A076410.

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: A084164 A036498 A248086 * A260658 A028281 A240102

Adjacent sequences:  A076406 A076407 A076408 * A076410 A076411 A076412

KEYWORD

nonn,easy

AUTHOR

R. K. Guy, Oct 08 2002

EXTENSIONS

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

STATUS

approved

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Last modified March 28 22:27 EDT 2017. Contains 284249 sequences.