A320423 Number of set partitions of {1,...,n} where each block's elements are pairwise coprime.

1, 1, 1, 2, 2, 8, 4, 28, 18, 120, 60, 888, 252, 5220, 1860, 22224, 9552, 311088, 59616

Offset

0,4

Comments

Two or more numbers are pairwise coprime if no pair of them has a common divisor > 1. A single number is not considered to be pairwise coprime unless it is equal to 1.

Links

Table of n, a(n) for n=0..18.

Example

The a(5) = 8 set partitions:
  {{1},{2,3},{4,5}}
  {{1},{2,5},{3,4}}
   {{1,2},{3,4,5}}
   {{1,4},{2,3,5}}
   {{1,2,3},{4,5}}
   {{1,2,5},{3,4}}
   {{1,3,4},{2,5}}
   {{1,4,5},{2,3}}

Mathematica

spsu[_, {}]:={{}}; spsu[foo_, set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]&/@spsu[Select[foo, Complement[#, Complement[set, s]]=={}&], Complement[set, s]]]/@Cases[foo, {i, ___}];
Table[Length[spsu[Select[Subsets[Range[n]], CoprimeQ@@#&], Range[n]]], {n, 10}]

Crossrefs

Cf. A000110, A051424, A084422, A085945, A186974, A187106, A302569, A302696, A303139, A303140, A320424, A320426, A320430, A320768.

Sequence in context: A337944 A103839 A135727 * A274449 A333711 A075101

Adjacent sequences: A320420 A320421 A320422 * A320424 A320425 A320426

Keyword

nonn,more

Author

Gus Wiseman, Jan 08 2019

Extensions

a(17)-a(18) from Alois P. Heinz, Jan 17 2019

Status

approved