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

Author

Gus Wiseman, Apr 19 2018

Keywords

• nonn

Examples

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

Crossrefs

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

Programs

Mathematica

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