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

Author

Gus Wiseman, Sep 18 2020

Keywords

• nonn

Comments

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

Examples

			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)
		

Links

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

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.

Programs

Mathematica

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

Formula

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