A282749 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).

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, 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, 7, 2, 4, 2, 3, 1, 2, 1, 1, 1, 1, 6, 2, 7, 2, 4, 2, 3, 1, 2, 1, 1, 1

Offset: 1

Author

N. J. A. Sloane, Mar 05 2017

Keywords

• nonn
• tabl

Comments

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

Examples

			Triangle begins:
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, 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, 7, 2, 4, 2, 3, 1, 2, 1, 1, 1,
1, 6, 2, 7, 2, 4, 2, 3, 1, 2, 1, 1, 1,
...
		

Links

• Alois P. Heinz, Rows n = 1..200, flattened (first 100 rows from Lars Blomberg)
• Temba Shonhiwa, Compositions with pairwise relatively prime summands within a restricted setting, Fibonacci Quart. 44 (2006), no. 4, 316-323.

Crossrefs

Cf. A051424 (row sums), A282749 (analog for compositions).

Formula

It seems that no general formula or recurrence is known.