A123175 Table (read by antidiagonals) where t(0,0)=1, t(m,n) = number of terms above and to the left of t(m,n) (i.e., number of t(k,j)'s, where 0 <= k <= m, 0 <= j <= n, excluding the t(m,n) case itself) which are coprime to (m+n).

1, 1, 1, 2, 3, 2, 3, 4, 4, 3, 3, 5, 4, 5, 3, 5, 8, 10, 10, 8, 5, 3, 5, 4, 5, 4, 5, 3, 7, 13, 17, 19, 19, 17, 13, 7, 7, 12, 12, 14, 13, 14, 12, 12, 7, 6, 12, 17, 21, 24, 24, 21, 17, 12, 6, 7, 10, 12, 14, 15, 13, 15, 14, 12, 10, 7, 11, 21, 29, 35, 39, 41, 41, 39, 35, 29, 21, 11, 7, 11, 13

Offset

0,4

Links

Table of n, a(n) for n=0..80.

Example

The first 4 columns and first 6 rows (excluding t(5,3)) of the table are:
  1,  1,  2,  3
  1,  3,  4,  5
  2,  4,  4, 10
  3,  5, 10,  5
  3,  8,  4, 19
  5,  5, 17,
The number of these terms which are coprime to (5+3) is 14 (the odd terms).
So t(5, 3) = 14.

Mathematica

t[0, 0] = 1; t[m_, n_] := t[m, n] = Block[{c = 0}, Do[ Do[ If[k == m && j == n, Continue[]]; If[GCD[t[k, j], m + n] == 1, c++ ]; , {j, 0, n}]; , {k, 0, m}]; c]; Flatten[Table[t[d - i, i], {d, 0, 12}, {i, 0, d}]] (* Ray Chandler, Nov 11 2006 *)

Crossrefs

Sequence in context: A303543 A124525 A106788 * A143998 A054237 A360495

Adjacent sequences: A123172 A123173 A123174 * A123176 A123177 A123178

Keyword

nonn,tabl

Author

Leroy Quet, Nov 04 2006

Extensions

Extended by Ray Chandler, Nov 11 2006

Status

approved