|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,6
|
|
LINKS
|
|
|
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.
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|