A337983 - OEIS

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A337983

Number of compositions of n into distinct parts, any two of which have a common divisor > 1.

1, 0, 1, 1, 1, 1, 3, 1, 3, 3, 5, 1, 13, 1, 13, 7, 19, 1, 35, 1, 59, 15, 65, 1, 117, 5, 133, 27, 195, 1, 411, 7, 435, 67, 617, 17, 941, 7, 1177, 135, 1571, 13, 2939, 31, 3299, 375, 4757, 13, 6709, 43, 8813, 643, 11307, 61, 16427, 123, 24331, 1203, 30461, 67

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OFFSET

0,7

COMMENTS

Number of pairwise non-coprime strict compositions of n.

LINKS

Table of n, a(n) for n=0..59.

EXAMPLE

The a(2) = 1 through a(15) = 7 compositions (A..F = 10..15):

2 3 4 5 6 7 8 9 A B C D E F

24 26 36 28 2A 2C 3C

42 62 63 46 39 4A 5A

64 48 68 69

82 84 86 96

93 A4 A5

A2 C2 C3

246 248

264 284

426 428

462 482

624 824

642 842

MATHEMATICA

stabQ[u_, Q_]:=And@@Not/@Q@@@Tuples[u, 2];

Table[Length[Join@@Permutations/@Select[IntegerPartitions[n], UnsameQ@@#&&stabQ[#, CoprimeQ]&]], {n, 0, 30}]

CROSSREFS

A318717 is the unordered version.

A318719 is the version for Heinz numbers of partitions.

A337561 is the pairwise coprime instead of pairwise non-coprime version, or A337562 if singletons are considered coprime.

A337605*6 counts these compositions of length 3.

A337667 is the non-strict version, ranked by A337666.

A337696 ranks these compositions.

A051185 and A305843 (covering) count pairwise intersecting set-systems.

A101268 counts pairwise coprime or singleton compositions.

A200976 and A328673 are the unordered version.

A233564 ranks strict compositions.

A318749 is the version for factorizations, with non-strict version A319786.

A333228 ranks compositions whose distinct parts are pairwise coprime.

A335236 ranks compositions neither a singleton nor pairwise coprime.

A337462 counts pairwise coprime compositions.

A337694 lists numbers with no two relatively prime prime indices.

Cf. A082024, A284825, A302797, A305713, A319752, A327516, A333227, A335235, A336737, A337604.

Sequence in context: A029153 A060241 A367951 * A332003 A145015 A085723

Adjacent sequences: A337980 A337981 A337982 * A337984 A337985 A337986

KEYWORD

nonn

AUTHOR

Gus Wiseman, Oct 06 2020

STATUS

approved