cp's OEIS Frontend

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

%I A320423 #17 Nov 28 2024 19:04:40
%S A320423 1,1,1,2,2,8,4,28,18,120,60,888,252,5220,1860,22224,9552,311088,59616,
%T A320423 2473056,565920,13627008,4051872,235039392,33805440,1932037632,
%U A320423 465239808,20604487680,4294865664,386228795904,35413136640
%N A320423 Number of set partitions of {1,...,n} where each block's elements are pairwise coprime.
%C A320423 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.
%e A320423 The a(5) = 8 set partitions:
%e A320423   {{1},{2,3},{4,5}}
%e A320423   {{1},{2,5},{3,4}}
%e A320423    {{1,2},{3,4,5}}
%e A320423    {{1,4},{2,3,5}}
%e A320423    {{1,2,3},{4,5}}
%e A320423    {{1,2,5},{3,4}}
%e A320423    {{1,3,4},{2,5}}
%e A320423    {{1,4,5},{2,3}}
%t A320423 spsu[_,{}]:={{}};spsu[foo_,set:{i_,___}]:=Join@@Function[s,Prepend[#,s]&/@spsu[Select[foo,Complement[#,Complement[set,s]]=={}&],Complement[set,s]]]/@Cases[foo,{i,___}];
%t A320423 Table[Length[spsu[Select[Subsets[Range[n]],CoprimeQ@@#&],Range[n]]],{n,10}]
%Y A320423 Cf. A000110, A051424, A084422, A085945, A186974, A187106, A302569, A302696, A303139, A303140, A320424, A320426, A320430, A320768.
%K A320423 nonn,more
%O A320423 0,4
%A A320423 _Gus Wiseman_, Jan 08 2019
%E A320423 a(17)-a(18) from _Alois P. Heinz_, Jan 17 2019
%E A320423 a(19)-a(30) from _Christian Sievers_, Nov 28 2024