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A320430
Number of set partitions of [n] where the elements of each non-singleton block are pairwise coprime.
6
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
0,3
COMMENTS
Two or more numbers are pairwise coprime if no pair of them has a common divisor > 1.
LINKS
EXAMPLE
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.
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}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 08 2019
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
STATUS
approved