

A195637


Number of distinct residues of k^n (mod n), k=0..n1.


23



1, 2, 3, 2, 5, 4, 7, 2, 3, 6, 11, 4, 13, 8, 15, 2, 17, 4, 19, 4, 9, 12, 23, 4, 5, 14, 3, 8, 29, 12, 31, 2, 33, 18, 35, 4, 37, 20, 15, 4, 41, 8, 43, 12, 15, 24, 47, 4, 7, 6, 51, 8, 53, 4, 15, 8, 21, 30, 59, 8, 61, 32, 9, 2, 65, 24, 67, 10, 69, 24, 71, 4, 73
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

a(n) = n if n prime.


LINKS



EXAMPLE

a(18) = 4 because k^18 == 0, 1, 9, 10 (mod 18) => 4 distinct residues.
The triangle of k^n (mod n) starts in row n=1 with columns k>=0 as:
0;
0, 1;
0, 1, 2;
0, 1, 0, 1;
0, 1, 2, 3, 4;
0, 1, 4, 3, 4, 1;
0, 1, 2, 3, 4, 5, 6;
0, 1, 0, 1, 0, 1, 0, 1;
0, 1, 8, 0, 1, 8, 0, 1, 8;
0, 1, 4, 9, 6, 5, 6, 9, 4, 1;
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10;
0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1;
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12;
Its row sums are 0, 1, 3, 2, 10, 13, 21, 4, 27, 45, 55, 38, 78, 77, 105, 8,.... (End)


MAPLE

a:= n> nops({seq(k&^n mod n, k=0..n1)}):
seq(a(n), n=1..100);


MATHEMATICA

Table[Length[Union[PowerMod[Range[0, n  1], n, n]]], {n, 100}] (* T. D. Noe, Sep 21 2011 *)


PROG

(Python)


CROSSREFS



KEYWORD

nonn,nice


AUTHOR



STATUS

approved



