

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).


0



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
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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 A129600
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



