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A326642
Number of non-constant integer partitions of n whose mean and geometric mean are both integers.
2
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 1, 1, 0, 0, 0, 4, 2, 0, 0, 3, 1, 2, 1, 2, 0, 7, 0, 4, 2, 2, 4, 7, 0, 0, 4, 12, 0, 9, 0, 2, 11, 0, 0, 17, 6, 14, 4, 8, 0, 13, 6, 27, 6, 2, 0, 36, 0, 0, 35, 32, 8, 20, 0, 11, 6, 56, 0, 91, 0, 2, 17
OFFSET
0,11
COMMENTS
The Heinz numbers of these partitions are given by A326646.
FORMULA
a(n) = A326641(n) - A000005(n).
EXAMPLE
The a(30) = 7 partitions:
(27,3)
(24,6)
(24,3,3)
(16,8,2,2,2)
(9,9,9,1,1,1)
(8,8,8,2,2,2)
(8,8,4,4,1,1,1,1,1,1)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], !SameQ@@#&&IntegerQ[Mean[#]]&&IntegerQ[GeometricMean[#]]&]], {n, 0, 30}]
CROSSREFS
Partitions with integer mean and geometric mean are A326641.
Heinz numbers of non-constant partitions with integer mean and geometric mean are A326646.
Non-constant partitions with integer geometric mean are A326624.
Sequence in context: A296238 A309475 A221314 * A087371 A307597 A307056
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 16 2019
STATUS
approved