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A326029
Number of strict integer partitions of n whose mean and geometric mean are both integers.
8
0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 1, 1, 1, 1, 3, 1, 2, 1, 3, 1, 1, 2, 3, 1, 3, 1, 1, 3, 6, 1, 3, 1, 2, 1, 1, 1, 3, 1, 6, 1, 5, 1, 2, 2, 2, 4, 3, 1, 9, 1, 1, 3, 1, 1, 4, 1, 4, 2, 6, 1, 6, 1, 3, 7, 4, 2, 5, 1, 10, 1, 3, 1, 9, 3
OFFSET
0,11
EXAMPLE
The a(55) = 2 through a(60) = 9 partitions:
(55) (56) (57) (58) (59) (60)
(27,16,9,2,1) (24,18,8,6) (49,7,1) (49,9) (54,6)
(27,25,5) (50,8) (48,12)
(27,18,12) (27,24,9)
(27,24,6,2,1)
(36,12,9,2,1)
(36,9,6,4,3,2)
(24,18,9,6,2,1)
(27,16,9,4,3,1)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&IntegerQ[Mean[#]]&&IntegerQ[GeometricMean[#]]&]], {n, 0, 30}]
CROSSREFS
Partitions with integer mean and geometric mean are A326641.
Strict partitions with integer mean are A102627.
Strict partitions with integer geometric mean are A326625.
Non-constant partitions with integer mean and geometric mean are A326641.
Subsets with integer mean and geometric mean are A326643.
Heinz numbers of partitions with integer mean and geometric mean are A326645.
Sequence in context: A074298 A356097 A356096 * A356167 A176028 A375391
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 16 2019
EXTENSIONS
More terms from Jinyuan Wang, Jun 26 2020
STATUS
approved