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

0,5

Links

Table of n, a(n) for n=0..65.

Example

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)

Mathematica

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

Crossrefs

Row sums of A319000.

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

Sequence in context: A277640 A370906 A165401 * A213074 A140966 A058036

Adjacent sequences: A319913 A319914 A319915 * A319917 A319918 A319919

Keyword

nonn

Author

Gus Wiseman, Oct 22 2018

Status

approved