login
A326625
Number of strict integer partitions of n whose geometric mean is an integer.
21
0, 1, 1, 1, 1, 2, 1, 2, 1, 1, 3, 1, 1, 3, 2, 2, 1, 2, 1, 2, 4, 3, 1, 2, 1, 4, 5, 2, 3, 3, 3, 5, 1, 3, 5, 5, 3, 4, 4, 7, 7, 5, 5, 2, 4, 2, 5, 7, 4, 6, 9, 5, 7, 7, 8, 7, 5, 11, 5, 9, 9, 9, 7, 9, 5, 13, 7, 9, 7, 11, 12, 7, 7, 12, 9, 13, 11, 10, 13, 7, 14
OFFSET
0,6
EXAMPLE
The a(63) = 9 partitions:
(63) (36,18,9) (54,4,3,2) (36,18,6,2,1) (36,9,8,6,3,1)
(48,12,3) (27,24,8,4) (18,16,12,9,8)
(32,18,9,4)
The initial terms count the following partitions:
1: (1)
2: (2)
3: (3)
4: (4)
5: (5)
5: (4,1)
6: (6)
7: (7)
7: (4,2,1)
8: (8)
9: (9)
10: (10)
10: (9,1)
10: (8,2)
11: (11)
12: (12)
13: (13)
13: (9,4)
13: (9,3,1)
14: (14)
14: (8,4,2)
15: (15)
15: (12,3)
16: (16)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&IntegerQ[GeometricMean[#]]&]], {n, 0, 30}]
CROSSREFS
Partitions whose geometric mean is an integer are A067539.
Strict partitions whose average is an integer are A102627.
Sequence in context: A368210 A233932 A008289 * A188884 A116679 A350032
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 14 2019
STATUS
approved