A066340 Fermat's triangle: T(n,m) = m^phi(n) mod n; n >= 2; 1 <= m <= n-1, where phi is Euler's totient function.

1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 4, 3, 4, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 6, 1, 6, 5, 6, 1, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 1, 8, 1, 8, 7, 8, 1, 8, 1, 8, 1, 1, 1, 6, 1, 10, 6, 1, 1, 6, 10, 1, 6, 1, 1

Offset

2,12

Comments

Fermat's little theorem states that T(n,m)=1 for all m relatively prime to n.

Links

Alois P. Heinz, Rows n = 2..201, flattened

Example

Triangle begins:
1;
1, 1;
1, 0, 1;
1, 1, 1, 1;
1, 4, 3, 4,  1;
1, 1, 1, 1,  1, 1;
1, 0, 1, 0,  1, 0, 1;
1, 1, 0, 1,  1, 0, 1, 1;
1, 6, 1, 6,  5, 6, 1, 6, 1;
1, 1, 1, 1,  1, 1, 1, 1, 1,  1;
1, 4, 9, 4,  1, 0, 1, 4, 9,  4, 1;
1, 1, 1, 1,  1, 1, 1, 1, 1,  1, 1, 1;
1, 8, 1, 8,  1, 8, 7, 8, 1,  8, 1, 8, 1;
1, 1, 6, 1, 10, 6, 1, 1, 6, 10, 1, 6, 1, 1;

Mathematica

Table[PowerMod[ #, EulerPhi[n], n]&/@ Range[n-1], {n, 2, 32} ]

Prog

(PARI) T(n, k) = lift(Mod(k, n)^eulerphi(n));
tabl(nn) = for (n=2, nn, for (k=1, n-1, print1(T(n, k), ", ")); print); \\ Michel Marcus, Aug 13 2019

Crossrefs

Cf. A000010.

Sequence in context: A048156 A070431 A070511 * A195597 A143505 A245727

Adjacent sequences: A066337 A066338 A066339 * A066341 A066342 A066343

Keyword

easy,nonn,tabl

Author

Wouter Meeussen, Jan 01 2002

Status

approved