%I #16 Jun 14 2017 22:20:14
%S 1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,2,1,1,1,1,3,1,2,1,1,1,1,2,3,1,2,1,
%T 1,1,1,3,2,3,1,2,1,1,1,1,2,4,2,3,1,2,1,1,1,1,5,2,4,2,3,1,2,1,1,1,1,2,
%U 7,2,4,2,3,1,2,1,1,1,1,6,2,7,2,4,2,3,1,2,1,1,1
%N Triangle read by rows: T(n,k) is the number of partitions of n into k parts x_1, x_2, ..., x_k such that gcd(x_i, x_j) = 1 for all i != j (where 1<=k<=n).
%C Column 2 is A023022. It appears that each row ends with some tail portion of the sequence (..., 89, 21, 89, 18, 68, 19, 53, 12, 58, 10, 40, 12, 30, 8, 31, 7, 20, 7, 17, 4, 16, 4, 9, 4, 8, 2, 7, 2, 4, 2, 3, 1, 2, 1, 1, 1). - _Lars Blomberg_ Mar 08 2017
%H Alois P. Heinz, <a href="/A282749/b282749.txt">Rows n = 1..200, flattened</a> (first 100 rows from Lars Blomberg)
%H Temba Shonhiwa, <a href="http://www.fq.math.ca/Papers1/44-4/quarttemba04_2006.pdf">Compositions with pairwise relatively prime summands within a restricted setting</a>, Fibonacci Quart. 44 (2006), no. 4, 316-323.
%F It seems that no general formula or recurrence is known.
%e Triangle begins:
%e 1,
%e 1, 1,
%e 1, 1, 1,
%e 1, 1, 1, 1,
%e 1, 2, 1, 1, 1,
%e 1, 1, 2, 1, 1, 1,
%e 1, 3, 1, 2, 1, 1, 1,
%e 1, 2, 3, 1, 2, 1, 1, 1,
%e 1, 3, 2, 3, 1, 2, 1, 1, 1,
%e 1, 2, 4, 2, 3, 1, 2, 1, 1, 1,
%e 1, 5, 2, 4, 2, 3, 1, 2, 1, 1, 1,
%e 1, 2, 7, 2, 4, 2, 3, 1, 2, 1, 1, 1,
%e 1, 6, 2, 7, 2, 4, 2, 3, 1, 2, 1, 1, 1,
%e ...
%Y Cf. A051424 (row sums), A282749 (analog for compositions).
%K nonn,tabl
%O 1,12
%A _N. J. A. Sloane_, Mar 05 2017