A337667 Number of compositions of n where any two parts have a common divisor > 1.

1, 0, 1, 1, 2, 1, 5, 1, 8, 4, 17, 1, 38, 1, 65, 19, 128, 1, 284, 1, 518, 67, 1025, 1, 2168, 16, 4097, 256, 8198, 1, 16907, 7, 32768, 1027, 65537, 79, 133088, 19, 262145, 4099, 524408, 25, 1056731, 51, 2097158, 16636, 4194317, 79, 8421248, 196, 16777712

Offset: 0

Author

Gus Wiseman, Oct 05 2020

Keywords

• nonn

Comments

First differs from A178472 at a(31) = 7, a(31) = 1.

Examples

			The a(2) = 1 through a(10) = 17 compositions (A = 10):
   2   3   4    5   6     7   8      9     A
           22       24        26     36    28
                    33        44     63    46
                    42        62     333   55
                    222       224          64
                              242          82
                              422          226
                              2222         244
                                           262
                                           424
                                           442
                                           622
                                           2224
                                           2242
                                           2422
                                           4222
                                           22222
		

Links

• Fausto A. C. Cariboni, Table of n, a(n) for n = 0..290

Crossrefs

A101268 = 1 + A337462 is the pairwise coprime version.

A328673 = A200976 + 1 is the unordered version.

A337604 counts these compositions of length 3.

A337666 ranks these compositions.

A337694 gives Heinz numbers of the unordered version.

A337983 is the strict case.

A051185 counts intersecting set-systems, with spanning case A305843.

A318717 is the unordered strict case.

A319786 is the version for factorizations, with strict case A318749.

A327516 counts pairwise coprime partitions.

A333227 ranks pairwise coprime compositions.

A333228 ranks compositions whose distinct parts are pairwise coprime.

Cf. A051424, A082024, A178472, A284825, A319752, A327039, A337599, A337605, A337665.

Programs

Mathematica

stabQ[u_,Q_]:=And@@Not/@Q@@@Tuples[u,2];
Table[Length[Join@@Permutations/@Select[IntegerPartitions[n],stabQ[#,CoprimeQ]&]],{n,0,15}]