A337562 Number of pairwise coprime strict compositions of n, where a singleton is always considered coprime.

1, 1, 1, 3, 3, 5, 9, 7, 17, 13, 23, 41, 41, 67, 49, 75, 75, 155, 211, 229, 243, 241, 287, 395, 807, 537, 841, 655, 1147, 1619, 2037, 2551, 2213, 2007, 2663, 4579, 4171, 7123, 4843, 6013, 6215, 11639, 13561, 16489, 14739, 15445, 16529, 25007, 41003, 32803

Offset

0,4

Links

Fausto A. C. Cariboni, Table of n, a(n) for n = 0..600

Formula

a(n > 1) = A337561(n) + 1 for n > 1.

Example

The a(1) = 1 through a(9) = 12 compositions:
  (1)  (2)  (3)    (4)    (5)    (6)      (7)    (8)      (9)
            (1,2)  (1,3)  (1,4)  (1,5)    (1,6)  (1,7)    (1,8)
            (2,1)  (3,1)  (2,3)  (5,1)    (2,5)  (3,5)    (2,7)
                          (3,2)  (1,2,3)  (3,4)  (5,3)    (4,5)
                          (4,1)  (1,3,2)  (4,3)  (7,1)    (5,4)
                                 (2,1,3)  (5,2)  (1,2,5)  (7,2)
                                 (2,3,1)  (6,1)  (1,3,4)  (8,1)
                                 (3,1,2)         (1,4,3)  (1,3,5)
                                 (3,2,1)         (1,5,2)  (1,5,3)
                                                 (2,1,5)  (3,1,5)
                                                 (2,5,1)  (3,5,1)
                                                 (3,1,4)  (5,1,3)
                                                 (3,4,1)  (5,3,1)
                                                 (4,1,3)
                                                 (4,3,1)
                                                 (5,1,2)
                                                 (5,2,1)

Mathematica

Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], UnsameQ@@#&&(Length[#]<=1||CoprimeQ@@#)&]], {n, 0, 10}]

Crossrefs

A007360 is the unordered version, with non-strict version A051424.

A101268 is the not necessarily strict version.

A220377*6 counts these compositions of length 3.

A337561 does not consider a singleton to be coprime unless it is (1), with non-strict version A337462.

A337664 looks only at distinct parts.

A000740 counts relatively prime compositions, with strict case A332004.

A072706 counts unimodal strict compositions.

A178472 counts compositions with a common factor.

A327516 counts pairwise coprime partitions, with strict case A305713.

A328673 counts pairwise non-coprime partitions.

A333228 ranks compositions whose distinct parts are pairwise coprime.

Cf. A087087, A220377, A302569, A307719, A326675, A333227, A335235, A335238, A337461, A337665.

Sequence in context: A098353 A073060 A183526 * A087343 A079586 A354953

Adjacent sequences: A337559 A337560 A337561 * A337563 A337564 A337565

Keyword

nonn

Author

Gus Wiseman, Sep 20 2020

Status

approved