A319916 Number of integer partitions of any number from 1 to n whose product of parts is n.

0, 1, 1, 1, 2, 1, 3, 1, 7, 5, 5, 1, 18, 1, 7, 9, 35, 1, 30, 1, 34, 13, 11, 1, 88, 17, 13, 36, 50, 1, 74, 1, 127, 21, 17, 25, 193, 1, 19, 25, 162, 1, 108, 1, 82, 96, 23, 1, 379, 37, 100, 33, 98, 1, 229, 41, 236, 37, 29, 1, 433, 1, 31, 140, 485, 49

Offset: 0

Author

Gus Wiseman, Oct 22 2018

Keywords

• nonn

Examples

			The sequence of integer partitions begins:
  (1)  (2)  (3)  (4)   (5)  (6)    (7)  (8)      (9)
                 (22)       (32)        (42)     (33)
                            (321)       (222)    (331)
                                        (421)    (3311)
                                        (2221)   (33111)
                                        (4211)
                                        (22211)
		

Crossrefs

Row sums of A319000.

Cf. A001055, A002865, A069016, A096276, A301987, A318950, A319005, A319057.

Programs

Mathematica

Table[Length[Select[Array[IntegerPartitions,n,1,Join],Times@@#==n&]],{n,30}]