A337462 Number of pairwise coprime compositions of n, where a singleton is not considered coprime unless it is (1).

1, 1, 1, 3, 6, 12, 21, 37, 62, 100, 159, 253, 402, 634, 983, 1491, 2224, 3280, 4813, 7043, 10270, 14888, 21415, 30585, 43400, 61204, 85747, 119295, 164834, 226422, 309663, 422301, 574826, 781236, 1060181, 1436367, 1942588, 2622078, 3531151, 4742315, 6348410

Offset

0,4

Comments

A composition of n is a finite sequence of positive integers summing to n.

Links

Fausto A. C. Cariboni, Table of n, a(n) for n = 0..500

Formula

For n > 1, a(n) = A101268(n) - 1.

Example

The a(1) = 1 through a(5) = 12 compositions:
  (1)  (1,1)  (1,2)    (1,3)      (1,4)
              (2,1)    (3,1)      (2,3)
              (1,1,1)  (1,1,2)    (3,2)
                       (1,2,1)    (4,1)
                       (2,1,1)    (1,1,3)
                       (1,1,1,1)  (1,3,1)
                                  (3,1,1)
                                  (1,1,1,2)
                                  (1,1,2,1)
                                  (1,2,1,1)
                                  (2,1,1,1)
                                  (1,1,1,1,1)

Mathematica

Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], #=={}||CoprimeQ@@#&]], {n, 0, 10}]

Crossrefs

A000740 counts the relatively prime instead of pairwise coprime version.

A101268 considers all singletons to be coprime, with strict case A337562.

A327516 is the unordered version.

A333227 ranks these compositions, with complement A335239.

A337461 counts these compositions of length 3.

A337561 is the strict case.

A051424 counts pairwise coprime or singleton partitions.

A101268 counts pairwise coprime or singleton compositions.

A178472 counts compositions with a common factor.

A305713 counts strict pairwise coprime partitions.

A328673 counts pairwise non-coprime partitions.

A333228 ranks compositions whose distinct parts are pairwise coprime.

A337667 counts pairwise non-coprime compositions.

Cf. A001523, A007360, A087087, A220377, A302569, A307719, A326675, A335235, A335238, A337664.

Sequence in context: A128128 A162920 A247662 * A215005 A006330 A293636

Adjacent sequences: A337459 A337460 A337461 * A337463 A337464 A337465

Keyword

nonn

Author

Gus Wiseman, Sep 18 2020

Status

approved