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A124524
Table (read by antidiagonals) where t(1,1) = 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 1 <= k <= m, 1 <= j <= n, excluding the t(m,n) case itself) which both divide m and are coprime to n.
1
1, 1, 1, 2, 3, 2, 3, 4, 4, 2, 2, 3, 3, 3, 2, 5, 3, 7, 6, 6, 2, 2, 7, 3, 3, 6, 3, 2, 5, 4, 6, 3, 9, 3, 8, 2, 3, 3, 5, 12, 3, 3, 8, 3, 2, 7, 9, 10, 5, 22, 3, 11, 9, 10, 2, 2, 5, 3, 3, 5, 3, 3, 3, 3, 3, 2, 8, 3, 12, 17, 12, 5, 30, 3, 13, 11, 12, 2, 2, 10, 3, 8, 19, 3, 3, 22, 3, 3, 11, 3, 2, 8, 3, 11, 3, 9, 3
OFFSET
1,4
EXAMPLE
The first 4 columns and first 6 rows (excluding t(6,4)) of the table are:
1, 1, 2, 2
1, 3, 4, 3
2, 4, 3, 6
3, 3, 7, 3
2, 3, 3, 3
5, 7, 6,
The number of these terms which both divide 6 and are coprime to 4 is 12 (the 1's and the 3's). So t(6,4) = 12.
MATHEMATICA
t[1, 1] = 1; t[m_, n_] := t[m, n] = Block[{c = 0}, Do[ Do[ If[k == m && j == n, Continue[]]; If[Mod[m, t[k, j]] == 0 && GCD[t[k, j], n] == 1, c++ ]; , {j, n}]; , {k, m}]; c]; Flatten[Table[t[d + 1 - i, i], {d, 14}, {i, d}]] (* Ray Chandler, Nov 11 2006 *)
CROSSREFS
Cf. A124525.
Sequence in context: A326820 A095161 A072106 * A303543 A124525 A106788
KEYWORD
nonn,tabl
AUTHOR
Leroy Quet, Nov 04 2006
EXTENSIONS
Extended by Ray Chandler, Nov 11 2006
STATUS
approved