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

%I A096103 #18 Feb 16 2025 08:32:53
%S A096103 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,
%T A096103 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,
%U A096103 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
%N A096103 Table read by rows: row n contains the quadratic residues modulo n which are coprime to n.
%C A096103 Each '1' begins a row.
%C A096103 Row lengths are A046073. - _Geoffrey Critzer_, Jan 02 2015
%H A096103 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/QuadraticResidue.html">Quadratic Residue</a>
%e A096103 1;
%e A096103 1;
%e A096103 1;
%e A096103 1,4;
%e A096103 1;
%e A096103 1, 2, 4;
%e A096103 1;
%e A096103 1, 4, 7;
%e A096103 1, 9;
%e A096103 1, 3, 4, 5, 9;
%e A096103 1;
%e A096103 1, 3, 4, 9, 10, 12;
%e A096103 1, 9, 11;
%e A096103 1, 4;
%t A096103 Table[Union[Mod[Select[Range[n], CoprimeQ[#, n] &]^2, n]], {n, 2, 20}] // Grid (* _Geoffrey Critzer_, Jan 02 2015 *)
%o A096103 (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]",")) ) ); ) }
%Y A096103 Cf. A046071, A046073.
%K A096103 nonn,tabf
%O A096103 2,5
%A A096103 _Cino Hilliard_, Jul 21 2004
%E A096103 Edited by _Don Reble_, Apr 16 2007