A320430 Number of set partitions of [n] where the elements of each non-singleton block are pairwise coprime.

1, 1, 2, 5, 10, 37, 60, 295, 658, 2621, 5368, 38535, 66506, 551529, 1234264, 5004697, 13721836, 143935131, 256835337, 2971237021, 6485081140, 35162930303, 95872321543, 1315397878401, 2399236456202, 25866803180347, 72374386475590, 563368417647305, 1479943119911866

Offset: 0

Author

Gus Wiseman, Jan 08 2019

Keywords

• nonn

Comments

Two or more numbers are pairwise coprime if no pair of them has a common divisor > 1.

Examples

			The a(4) = 10 set partitions: 1|2|3|4, 14|2|3, 13|2|4, 12|3|4, 1|23|4, 1|2|34, 134|2, 123|4, 14|23, 12|34.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..38

Crossrefs

Cf. A000110, A000258, A008277, A051424, A085945, A186974, A187106, A302569, A303139, A320424, A320426, A320423, A333517.

Programs

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]],Length[#]==1||CoprimeQ@@#&],Range[n]]],{n,10}]

Extensions

a(14)-a(15) from Alois P. Heinz, Jan 08 2019

a(16) from Alois P. Heinz, Mar 26 2020

a(17)-a(24) from Giovanni Resta, Mar 27 2020

a(25)-a(28) from Alois P. Heinz, Aug 03 2023