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 A326641 Number of integer partitions of n whose mean and geometric mean are both integers. 11
 0, 1, 2, 2, 3, 2, 4, 2, 4, 3, 6, 2, 7, 2, 4, 5, 6, 2, 6, 2, 10, 6, 4, 2, 11, 4, 6, 5, 8, 2, 15, 2, 10, 6, 6, 8, 16, 2, 4, 8, 20, 2, 17, 2, 8, 17, 4, 2, 27, 9, 20, 8, 14, 2, 21, 10, 35, 10, 6, 2, 48, 2, 4, 41, 39, 12, 28, 2, 17, 10, 64, 2, 103, 2, 6, 23 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS The Heinz numbers of these partitions are given by A326645. LINKS Wikipedia, Geometric mean EXAMPLE The a(4) = 3 through a(10) = 6 partitions (A = 10):   (4)     (5)      (6)       (7)        (8)         (9)          (A)   (22)    (11111)  (33)      (1111111)  (44)        (333)        (55)   (1111)           (222)                (2222)      (111111111)  (82)                    (111111)             (11111111)               (91)                                                                  (22222)                                                                  (1111111111) MATHEMATICA Table[Length[Select[IntegerPartitions[n], IntegerQ[Mean[#]]&&IntegerQ[GeometricMean[#]]&]], {n, 0, 30}] CROSSREFS Partitions with integer mean are A067538. Partitions with integer geometric mean are A067539. Non-constant partitions with integer mean and geometric mean are A326642. Subsets with integer mean and geometric mean are A326643. Heinz numbers of partitions with integer mean and geometric mean are A326645. Strict partitions with integer mean and geometric mean are A326029. Cf. A051293, A078175, A082553, A102627, A316413, A326027, A326623, A326644, A326646, A326647. Sequence in context: A169819 A134681 A218703 * A144372 A182861 A049238 Adjacent sequences:  A326638 A326639 A326640 * A326642 A326643 A326644 KEYWORD nonn AUTHOR Gus Wiseman, Jul 16 2019 STATUS approved

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Last modified May 7 02:20 EDT 2021. Contains 343636 sequences. (Running on oeis4.)