A095972 Number of quadratic nonresidues modulo n.

0, 0, 1, 2, 2, 2, 3, 5, 5, 4, 5, 8, 6, 6, 9, 12, 8, 10, 9, 14, 13, 10, 11, 18, 14, 12, 16, 20, 14, 18, 15, 25, 21, 16, 23, 28, 18, 18, 25, 31, 20, 26, 21, 32, 33, 22, 23, 40, 27, 28, 33, 38, 26, 32, 37, 44, 37, 28, 29, 48, 30, 30, 47, 52, 44, 42, 33, 50, 45, 46, 35, 60, 36, 36, 53

Offset

1,4

Comments

A218578(n) is the number of times n occurs in this sequence. - Dmitri Kamenetsky, Nov 03 2012

Links

T. D. Noe, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Quadratic Nonresidue

Formula

a(n) = n - A000224(n). - R. J. Mathar, Nov 05 2012

Maple

A095972 := proc(n)
    local a, q;
    a := 0 ;
    for q from 0 to n-1 do
        if numtheory[quadres](q, n) = -1 then
            a := a+1 ;
        end if;
    end do;
    a ;
end proc: # R. J. Mathar, Nov 05 2012

Mathematica

Table[Length[Complement[Range[n-1], Union[Mod[Range[n]^2, n]]]], {n, 100}] (* T. D. Noe, Nov 06 2012 *)

Prog

(PARI) A095972(n)={local(v); v=vector(n, i, 1); for(i=0, floor(n/2), v[i^2%n+1]=0); sum(i=1, n, v[i])} \\ Michael B. Porter, Apr 30 2010
(PARI) a(n)=my(f=factor(n)); n-prod(i=1, #f[, 1], if(f[i, 1]==2, 2^f[1, 2]\6+2, f[i, 1]^(f[i, 2]+1)\(2*f[i, 1]+2)+1)) \\ Charles R Greathouse IV, Jul 15 2011
(Python)
from math import prod
from sympy import factorint
def A095972(n): return n-prod((p**(e+1)//((p+1)*(q:=1+(p==2)))>>1)+q for p, e in factorint(n).items()) # Chai Wah Wu, Oct 07 2024

Crossrefs

Cf. A096013, A218578.

Sequence in context: A036355 A228390 A309256 * A091974 A029073 A376812

Adjacent sequences: A095969 A095970 A095971 * A095973 A095974 A095975

Keyword

nonn

Author

Cino Hilliard, Jul 21 2004

Extensions

Edited by Don Reble, May 07 2006

Status

approved