A337697 Number of pairwise coprime compositions of n with no 1's, where a singleton is not considered coprime.

0, 0, 0, 0, 0, 2, 0, 4, 2, 4, 8, 8, 14, 10, 16, 12, 30, 38, 46, 46, 48, 52, 62, 152, 96, 156, 112, 190, 256, 338, 420, 394, 326, 402, 734, 622, 1150, 802, 946, 898, 1730, 1946, 2524, 2200, 2328, 2308, 3356, 5816, 4772, 5350, 4890, 6282, 6316, 12092, 8902

Offset

0,6

Comments

A composition of n is a finite sequence of positive integers summing to n. These compositions must be strict.

Links

Table of n, a(n) for n=0..54.

Formula

For n > 1, the version where singletons are considered coprime is a(n) + 1.

Example

The a(5) = 2 through a(12) = 14 compositions (empty column indicated by dot):
  (2,3)  .  (2,5)  (3,5)  (2,7)  (3,7)    (2,9)  (5,7)
  (3,2)     (3,4)  (5,3)  (4,5)  (7,3)    (3,8)  (7,5)
            (4,3)         (5,4)  (2,3,5)  (4,7)  (2,3,7)
            (5,2)         (7,2)  (2,5,3)  (5,6)  (2,7,3)
                                 (3,2,5)  (6,5)  (3,2,7)
                                 (3,5,2)  (7,4)  (3,4,5)
                                 (5,2,3)  (8,3)  (3,5,4)
                                 (5,3,2)  (9,2)  (3,7,2)
                                                 (4,3,5)
                                                 (4,5,3)
                                                 (5,3,4)
                                                 (5,4,3)
                                                 (7,2,3)
                                                 (7,3,2)

Mathematica

Table[Length[Join@@Permutations/@Select[IntegerPartitions[n], !MemberQ[#, 1]&&CoprimeQ@@#&]], {n, 0, 30}]

Crossrefs

A022340 intersected with A333227 is a ranking sequence (using standard compositions A066099) for these compositions.

A212804 does not require coprimality, with unordered version A002865.

A337450 is the relatively prime instead of pairwise coprime version, with strict case A337451 and unordered version A302698.

A337462 allows 1's, with strict case A337561 (or A101268 with singletons), unordered version A327516 with Heinz numbers A302696, and 3-part case A337461.

A337485 is the unordered version (or A007359 with singletons considered coprime), with Heinz numbers A337984.

A337563 is the case of unordered triples.

Cf. A078374, A178472, A302568, A302697, A305713, A307719, A332004, A337562.

Sequence in context: A196606 A371130 A361391 * A328599 A222303 A097945

Adjacent sequences: A337694 A337695 A337696 * A337698 A337699 A337700

Keyword

nonn

Author

Gus Wiseman, Oct 06 2020

Status

approved