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A320430 Number of set partitions of {1,...,n} where the elements of each non-singleton block are pairwise coprime. 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

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

LINKS

Table of n, a(n) for n=0..24.

EXAMPLE

The a(4) = 10 set partitions:

  {{1},{2},{3},{4}}

   {{1,4},{2},{3}}

   {{1,3},{2},{4}}

   {{1,2},{3},{4}}

   {{1},{2,3},{4}}

   {{1},{2},{3,4}}

    {{1,3,4},{2}}

    {{1,2,3},{4}}

    {{1,4},{2,3}}

    {{1,2},{3,4}}

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}]

CROSSREFS

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

Sequence in context: A056300 A326006 A144636 * A018418 A290032 A155217

Adjacent sequences:  A320427 A320428 A320429 * A320431 A320432 A320433

KEYWORD

nonn,more,changed

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

STATUS

approved

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Last modified April 7 04:20 EDT 2020. Contains 333292 sequences. (Running on oeis4.)