A319330 Number of integer partitions of n whose length is equal to the GCD of the parts and whose sum is equal to the LCM of the parts.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 3, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 1, 0, 1, 0, 3, 0, 0, 0, 0, 2

Offset: 1

Author

Gus Wiseman, Sep 17 2018

Keywords

• nonn

Examples

			A list of all such partitions begins (1), (9,6,3), (20,8,8,4), (24,16,4,4), (16,16,12,4), (16,12,12,8), (25,10,5,5,5), (20,15,15,5,5), (20,15,10,10,5).
		

Crossrefs

Cf. A067538, A074761, A143773, A316432, A319328, A319329, A319333.

Programs

Mathematica

Table[Length[Select[IntegerPartitions[n],And[LCM@@#==Total[#],GCD@@#==Length[#]]&]],{n,30}]

Extensions

a(71)-a(105) from Alois P. Heinz, Sep 18 2018