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

1,48

Links

Table of n, a(n) for n=1..105.

Example

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).

Mathematica

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

Crossrefs

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

Sequence in context: A009138 A175562 A373202 * A291204 A331414 A111025

Adjacent sequences: A319327 A319328 A319329 * A319331 A319332 A319333

Keyword

nonn

Author

Gus Wiseman, Sep 17 2018

Extensions

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

Status

approved