|
|
A303140
|
|
Number of strict integer partitions of n with at least two but not all parts having a common divisor greater than 1.
|
|
15
|
|
|
0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 4, 2, 8, 7, 14, 14, 21, 18, 33, 32, 50, 54, 72, 67, 103, 110, 145, 155, 201, 196, 271, 293, 372, 400, 493, 512, 647, 704, 858, 924, 1115, 1167, 1436, 1560, 1854, 2022, 2368, 2510, 3005, 3255, 3804, 4144, 4792, 5116, 5989, 6514, 7486
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,9
|
|
LINKS
|
|
|
EXAMPLE
|
The a(14) = 7 partitions are (932), (8321), (7421), (653), (6521), (6431), (5432).
|
|
MATHEMATICA
|
Table[Select[IntegerPartitions[n], UnsameQ@@#&&!CoprimeQ@@#&&GCD@@#===1&]//Length, {n, 20}]
|
|
CROSSREFS
|
Cf. A000837, A018783, A051424, A078374, A168532, A289508, A289509, A298748, A300486, A302569, A302696, A302796, A303138, A303139.
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|