A303139 Number of integer partitions of n with at least two but not all parts having a common divisor greater than 1.

0, 0, 0, 0, 1, 1, 5, 6, 13, 17, 33, 37, 68, 82, 125, 159, 237, 278, 409, 491, 674, 830, 1121, 1329, 1781, 2144, 2770, 3345, 4299, 5086, 6507, 7752, 9687, 11571, 14378, 16985, 21039, 24876, 30379, 35924, 43734, 51320, 62238, 73068, 87747, 103021, 123347, 143955

Offset

1,7

Links

Table of n, a(n) for n=1..48.

Example

The a(7) = 5 partitions are (421), (331), (322), (2221), (22111).

Mathematica

Table[Select[IntegerPartitions[n], !CoprimeQ@@#&&GCD@@#===1&]//Length, {n, 30}]

Crossrefs

Cf. A000837, A018783, A051424, A078374, A168532, A289508, A289509, A298748, A300486, A302569, A302696, A302796, A303138, A303140.

Sequence in context: A059176 A219978 A326657 * A322611 A030356 A138937

Adjacent sequences: A303136 A303137 A303138 * A303140 A303141 A303142

Keyword

nonn

Author

Gus Wiseman, Apr 19 2018

Status

approved