A096103 Table read by rows: row n contains the quadratic residues modulo n which are coprime to n.

1, 1, 1, 1, 4, 1, 1, 2, 4, 1, 1, 4, 7, 1, 9, 1, 3, 4, 5, 9, 1, 1, 3, 4, 9, 10, 12, 1, 9, 11, 1, 4, 1, 9, 1, 2, 4, 8, 9, 13, 15, 16, 1, 7, 13, 1, 4, 5, 6, 7, 9, 11, 16, 17, 1, 9, 1, 4, 16, 1, 3, 5, 9, 15, 1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18, 1, 1, 4, 6, 9, 11, 14, 16, 19, 21, 24, 1, 3, 9, 17, 23, 25, 1, 4

Offset

2,5

Comments

Each '1' begins a row.

Row lengths are A046073. - Geoffrey Critzer, Jan 02 2015

Links

Table of n, a(n) for n=2..95.

Eric Weisstein's World of Mathematics, Quadratic Residue

Example

1;
1;
1;
1,4;
1;
1, 2, 4;
1;
1, 4, 7;
1, 9;
1, 3, 4, 5, 9;
1;
1, 3, 4, 9, 10, 12;
1, 9, 11;
1, 4;

Mathematica

Table[Union[Mod[Select[Range[n], CoprimeQ[#, n] &]^2, n]], {n, 2, 20}] // Grid (* Geoffrey Critzer, Jan 02 2015 *)

Prog

(PARI) maybesqgcd1(n) = { for(x=2, n, b=floor(x/2); a=vector(b+1); for(y=1, b, z=y^2%x; if(z<>0, a[y]=z; ) ); s=vecsort(a); c=1; for(j=2, b+1, if(s[j]<>s[j-1], c++; if(gcd(x, s[j])==1, print1(s[j]", ")) ) ); ) }

Crossrefs

Cf. A046071, A046073.

Sequence in context: A325529 A264534 A228489 * A204456 A143441 A279206

Adjacent sequences: A096100 A096101 A096102 * A096104 A096105 A096106

Keyword

nonn,tabf

Author

Cino Hilliard, Jul 21 2004

Extensions

Edited by Don Reble, Apr 16 2007

Status

approved