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%I #12 Jul 22 2017 08:32:32
%S 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,
%T 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,
%U 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
%N 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.
%e The first 4 columns and first 6 rows (excluding t(6,4)) of the table are:
%e 1, 1, 2, 2
%e 1, 3, 4, 3
%e 2, 4, 3, 6
%e 3, 3, 7, 3
%e 2, 3, 3, 3
%e 5, 7, 6,
%e 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.
%t 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 *)
%Y Cf. A124525.
%K nonn,tabl
%O 1,4
%A _Leroy Quet_, Nov 04 2006
%E Extended by _Ray Chandler_, Nov 11 2006