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

Author

Cino Hilliard, Jul 21 2004

Keywords

• nonn
• tabf

Comments

Each '1' begins a row.

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

Examples

			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;
		

Links

• Eric Weisstein's World of Mathematics, Quadratic Residue

Crossrefs

Cf. A046071, A046073.

Programs

Mathematica

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

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]",")) ) ); ) }

Extensions

Edited by Don Reble, Apr 16 2007