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 A316465 Heinz numbers of integer partitions such that every nonempty submultiset has an integer average. 1
 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 16, 17, 19, 21, 22, 23, 25, 27, 29, 31, 32, 34, 37, 39, 41, 43, 46, 47, 49, 53, 55, 57, 59, 61, 62, 64, 67, 68, 71, 73, 79, 81, 82, 83, 85, 87, 89, 91, 94, 97, 101, 103, 107, 109, 110, 111, 113, 115, 118, 121, 125, 127, 128 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k). Supersequence of A000961. - David A. Corneth, Jul 06 2018 LINKS EXAMPLE Sequence of partitions begins (), (1), (2), (1,1), (3), (4), (1,1,1), (2,2), (3,1), (5), (6), (1,1,1,1), (7), (8), (4,2), (5,1), (9), (3,3), (2,2,2). MATHEMATICA Select[Range[100], And@@IntegerQ/@Mean/@Union[Rest[Subsets[If[#==1, {}, Flatten[Cases[FactorInteger[#], {p_, k_}:>Table[PrimePi[p], {k}]]]]]]]&] CROSSREFS Cf. A056239, A067538, A122768, A237984, A296150, A316313, A316314, A316440, A316557. Sequence in context: A324758 A305504 A316413 * A004764 A128649 A032894 Adjacent sequences:  A316462 A316463 A316464 * A316466 A316467 A316468 KEYWORD nonn AUTHOR Gus Wiseman, Jul 06 2018 STATUS approved

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Last modified April 5 06:13 EDT 2020. Contains 333238 sequences. (Running on oeis4.)