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

1,12

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

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.

Formula

It seems that no general formula or recurrence is known.

Example

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,
...

Crossrefs

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

Sequence in context: A074971 A344008 A198067 * A132587 A318930 A235748

Adjacent sequences: A282746 A282747 A282748 * A282750 A282751 A282752

Keyword

nonn,tabl

Author

N. J. A. Sloane, Mar 05 2017

Status

approved