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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 Table of n, a(n) for n=0..60. 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 April 23 03:29 EDT 2024. Contains 371906 sequences. (Running on oeis4.)