A333389 Triangle read by rows: T(n,k) is the number of solutions to x^y == k (mod n) for n >= 1, k >= 0, where 0 <= x < n and 1 <= y <= n.

1, 2, 2, 3, 4, 2, 7, 6, 1, 2, 5, 9, 3, 3, 5, 6, 9, 3, 6, 9, 3, 7, 16, 7, 3, 7, 3, 6, 27, 20, 1, 4, 3, 4, 1, 4, 25, 21, 3, 1, 9, 3, 1, 9, 9, 10, 19, 5, 5, 11, 10, 19, 5, 5, 11, 11, 28, 5, 13, 13, 13, 5, 5, 5, 13, 10, 23, 30, 1, 6, 35, 6, 1, 6, 11, 18, 1, 6

Offset

1,2

Comments

T(n,0) = A333386(n);

T(n,1) = A333387(n) for n >= 2;

T(n,n-1) = A333388(n).

Links

Table of n, a(n) for n=1..78.

Example

Triangle T(n,k) begins:
n\k  0  1  2  3  4  5  6  7  8  9 10
1:   1
2:   2  2
3:   3  4  2
4:   7  6  1  2
5:   5  9  3  3  5
6:   6  9  3  6  9  3
7:   7 16  7  3  7  3  6
8:  27 20  1  4  3  4  1  4
9:  25 21  3  1  9  3  1  9  9
10: 10 19  5  5 11 10 19  5  5 11
11: 11 28  5 13 13 13  5  5  5 13 10
...
T(5,2) = 3 because the equation x^y == 2 (mod 5) has the 3 solutions 2^1 == 2 (mod 5), 3^3 == 2 (mod 5) and 2^5 == 2 (mod 5).

Prog

(PARI) T(n, k) = sum(x=0, n-1, sum (y=1, n, Mod(x, n)^y == k)); \\ Michel Marcus, Mar 26 2020

Crossrefs

Cf. A333386, A333387, A333388.

Sequence in context: A325785 A207632 A175503 * A352286 A352259 A375207

Adjacent sequences: A333386 A333387 A333388 * A333390 A333391 A333392

Keyword

nonn,tabl

Author

Franz Vrabec, Mar 24 2020

Status

approved