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A096107 Triangle read by rows: row n lists cubic residues modulo n. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 22 21:47 EST 2022. Contains 350504 sequences. (Running on oeis4.)