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

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, 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, 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

Offset

2,3

Comments

Row n has A087692(n) terms. - Robert Israel, Jan 04 2015

Links

Table of n, a(n) for n=2..94.

Example

1;
1,2;
1,3;
1,2,3,4;
1,5;
1,6;
1,3,5,7;
1,8;
1,3,7,9;
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

Maple

for n from 2 to 30 do
  op({seq(`if`(igcd(i, n)=1, i^3 mod n, NULL), i=1..n-1)})
# if using Maple 11 or earlier, replace this by
#   op(sort(convert({seq(`if`(igcd(i, n)=1, i^3 mod n, NULL), i=1..n-1)}, list)))
od; # Robert Israel, Jan 04 2015

Mathematica

Table[Select[Range[n],
   CoprimeQ[#, n] && IntegerQ[PowerMod[#, 1/3, n]] &], {n, 1, 20}] // Grid
(* Geoffrey Critzer, Jan 04 2015 *)

Prog

(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]", ")) ) ); ) }

Crossrefs

Cf. A087692, A096087.

Sequence in context: A038566 A020652 A293248 * A329585 A128487 A056609

Adjacent sequences: A096104 A096105 A096106 * A096108 A096109 A096110

Keyword

nonn,tabf

Author

Cino Hilliard, Jul 22 2004

Extensions

Edited by Don Reble, May 07 2006

Status

approved