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A326641
Number of integer partitions of n whose mean and geometric mean are both integers.
18
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
OFFSET
0,3
COMMENTS
The Heinz numbers of these partitions are given by A326645.
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.
Sequence in context: A373738 A134681 A218703 * A144372 A182861 A049238
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 16 2019
STATUS
approved