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A096107 Triangle read by rows: row n lists cubic residues modulo n.

%I A096107 #34 Sep 05 2018 08:28:16
%S A096107 1,1,2,1,3,1,2,3,4,1,5,1,6,1,3,5,7,1,8,1,3,7,9,1,2,3,4,5,6,7,8,9,10,1,
%T A096107 5,7,11,1,5,8,12,1,13,1,2,4,7,8,11,13,14,1,3,5,7,9,11,13,15,1,2,3,4,5,
%U A096107 6,7,8,9,10,11,12,13,14,15,16,1,17,1,7,8,11,12,18,1,3,7,9,11,13,17,19,1,8
%N A096107 Triangle read by rows: row n lists cubic residues modulo n.
%C A096107 Row n has A087692(n) terms. - _Robert Israel_, Jan 04 2015
%e A096107 1;
%e A096107 1,2;
%e A096107 1,3;
%e A096107 1,2,3,4;
%e A096107 1,5;
%e A096107 1,6;
%e A096107 1,3,5,7;
%e A096107 1,8;
%e A096107 1,3,7,9;
%e A096107 Row 5 contains 1,2,3,4 because (in mod 5)  1^3 = 1, 3^3 = 2, 2^3 = 3, and 4^3 = 4. - _Geoffrey Critzer_, Jan 07 2015
%p A096107 for n from 2 to 30 do
%p A096107   op({seq(`if`(igcd(i,n)=1,i^3 mod n,NULL),i=1..n-1)})
%p A096107 # if using Maple 11 or earlier, replace this by
%p A096107 #   op(sort(convert({seq(`if`(igcd(i,n)=1,i^3 mod n,NULL),i=1..n-1)},list)))
%p A096107 od; # _Robert Israel_, Jan 04 2015
%t A096107 Table[Select[Range[n],
%t A096107    CoprimeQ[#, n] && IntegerQ[PowerMod[#, 1/3, n]] &], {n, 1, 20}] // Grid
%t A096107 (* _Geoffrey Critzer_, Jan 04 2015 *)
%o A096107 (PARI) maybecubegcd1(n) = { for(x=2,n, b=floor(x-1); a=vector(b+1); for(y=1,b, z=y^3%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(s[j],x)==1,print1(s[j]",")) ) ); ) }
%Y A096107 Cf. A087692, A096087.
%K A096107 nonn,tabf
%O A096107 2,3
%A A096107 _Cino Hilliard_, Jul 22 2004
%E A096107 Edited by _Don Reble_, May 07 2006