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 A316440 Number of integer partitions of n such that every submultiset has an integer average. 5
 1, 1, 2, 2, 4, 2, 6, 2, 7, 5, 8, 2, 13, 2, 10, 10, 14, 2, 20, 2, 17, 15, 14, 2, 32, 3, 16, 22, 25, 2, 40, 2, 27, 30, 20, 4, 58, 2, 22, 40, 40, 2, 64, 2, 40, 53, 26, 2, 93, 3, 30, 64, 54, 2, 94, 4, 58, 78, 32, 2, 138, 2, 34, 96, 75, 10, 131, 2, 76, 111, 48, 2, 192, 2, 40, 138, 99 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Max Alekseyev, Table of n, a(n) for n = 0..500 FORMULA For a prime p, a(p) = 2. - Max Alekseyev, Sep 02 2023 EXAMPLE The a(12) = 13 partitions: (12), (6,6), (7,5), (8,4), (9,3), (10,2), (11,1), (4,4,4), (6,4,2), (8,2,2), (3,3,3,3), (2,2,2,2,2,2), (1,1,1,1,1,1,1,1,1,1,1,1). MATHEMATICA Table[Length[Select[IntegerPartitions[n], And@@IntegerQ/@Mean/@Union[Rest[Subsets[#]]]&]], {n, 20}] CROSSREFS Cf. A067538, A074761, A122768, A143773, A237984, A298423, A316313, A316314. Sequence in context: A360593 A080221 A137849 * A118982 A129457 A275365 Adjacent sequences: A316437 A316438 A316439 * A316441 A316442 A316443 KEYWORD nonn AUTHOR Gus Wiseman, Jul 03 2018 EXTENSIONS a(0) prepended and more terms added by Max Alekseyev, Sep 02 2023 STATUS approved

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Last modified June 20 17:22 EDT 2024. Contains 373530 sequences. (Running on oeis4.)