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 A328871 Number of integer partitions of n whose distinct parts are pairwise indivisible (stable) and pairwise non-relatively prime (intersecting). 1
 1, 1, 2, 2, 3, 2, 4, 2, 4, 3, 5, 2, 6, 2, 7, 5, 7, 2, 10, 2, 11, 7, 14, 2, 16, 4, 19, 8, 22, 2, 30, 3, 29, 14, 37, 8, 48, 4, 50, 19, 59, 5, 82, 4, 81, 28, 93, 8, 128, 9, 128, 38, 147, 8, 199, 19, 196, 52, 223, 12, 308 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS A partition with no two distinct parts divisible is said to be stable, and a partition with no two distinct parts relatively prime is said to be intersecting, so these are just stable intersecting partitions. LINKS EXAMPLE The a(1) = 1 through a(10) = 5 partitions (A = 10):   1  2   3    4     5      6       7        8         9          A      11  111  22    11111  33      1111111  44        333        55               1111         222              2222      111111111  64                            111111           11111111             22222                                                                  1111111111 MATHEMATICA stableQ[u_, Q_]:=!Apply[Or, Outer[#1=!=#2&&Q[#1, #2]&, u, u, 1], {0, 1}]; Table[Length[Select[IntegerPartitions[n], stableQ[Union[#], Divisible]&&stableQ[Union[#], GCD[#1, #2]==1&]&]], {n, 0, 30}] CROSSREFS The Heinz numbers of these partitions are A329366. Replacing "intersecting" with "relatively prime" gives A328676. Stable partitions are A305148. Intersecting partitions are A328673. Cf. A000837, A285573, A303362, A305148, A316476, A328671, A328677. Sequence in context: A076640 A326198 A324105 * A169819 A134681 A218703 Adjacent sequences:  A328868 A328869 A328870 * A328872 A328873 A328874 KEYWORD nonn AUTHOR Gus Wiseman, Nov 12 2019 STATUS approved

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Last modified December 1 06:09 EST 2020. Contains 338833 sequences. (Running on oeis4.)