A303140 Number of strict integer partitions of n with at least two but not all parts having a common divisor greater than 1.

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

Offset

1,9

Links

Table of n, a(n) for n=1..57.

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.

Sequence in context: A338042 A131999 A113416 * A370469 A103178 A173300

Adjacent sequences: A303137 A303138 A303139 * A303141 A303142 A303143

Keyword

nonn

Author

Gus Wiseman, Apr 19 2018

Status

approved