A232505 Sum of odd quadratic residues of prime(n).
1, 1, 1, 1, 18, 13, 38, 50, 26, 83, 66, 137, 224, 242, 147, 303, 509, 395, 578, 364, 714, 563, 965, 1046, 1254, 1155, 1043, 1565, 1323, 1676, 1667, 2440, 2456, 2589, 2563, 2284, 2827, 3362, 2526, 3503, 4408, 3765, 3271, 4902, 4557, 4005, 5829, 5380, 6952, 6093, 7046, 5288, 7626, 8691, 8552, 6871, 8563, 7622, 9007, 10250, 10365, 10233
Offset: 1
Keywords
Examples
a(1), a(2), a(3) and a(4) are all 1, as for the corresponding primes 2, 3, 5 and 7 the quadratic residue sets are {1}, {1}, {1,4} and {1,2,4}, in which all cases, only 1 is an odd residue.
For a(5), which is computed for the 5th prime, 11, we have a set of its quadratic residues (those less than 11) as {1,3,4,5,9}, of which when we sum only the odd residues, 1+3+5+9, we get a(5) = 18.
Links
- Indranil Ghosh, Table of n, a(n) for n = 1..1000
- Wikipedia, Quadratic residue
Programs
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Mathematica
Table[Function[p, Total@ Select[Range[1, p, 2], JacobiSymbol[#, p] == 1 &]]@ Prime@ n, {n, 62}] (* Michael De Vlieger, May 14 2017 *) -
PARI
A232597(n) = {s=0; for(k=1, n, s=s+((k%2)*((1+kronecker(k, n))\2)*k)); return(s); } forprime (i=1, 300, print1(A232597(i), ", ")) \\ Antti Karttunen, Nov 26 2013
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Python
from sympy.ntheory.residue_ntheory import quadratic_residues as q from sympy import prime def a(n): return sum(i for i in q(prime(n)) if i%2) print([a(n) for n in range(1, 101)]) # Indranil Ghosh, May 14 2017
Formula
Extensions
Missing 1 (as a(1) is value for the first prime, 2) inserted into beginning by Antti Karttunen, Nov 26 2013
Comments