A335405 Number of integer compositions of n with product n.

0, 1, 1, 1, 2, 1, 7, 1, 23, 11, 21, 1, 241, 1, 43, 73, 1092, 1, 1041, 1, 1339, 157, 111, 1, 23023, 137, 157, 1603, 3945, 1, 11599, 1, 153446, 421, 273, 601, 204586, 1, 343, 601, 206351, 1, 34789, 1, 16273, 25179, 507, 1, 5992730, 667, 33913, 1057, 27291, 1

Offset

0,5

Comments

A composition of n is a finite sequence of positive integers summing to n.

Links

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Example

The compositions for n = 1, 4, 6, 8, 9, 10:
  (1)  (4)   (6)    (8)      (9)      (10)
       (22)  (123)  (1124)   (11133)  (11125)
             (132)  (1142)   (11313)  (11152)
             (213)  (1214)   (11331)  (11215)
             (231)  (1241)   (13113)  (11251)
             (312)  (1412)   (13131)  (11512)
             (321)  (1421)   (13311)  (11521)
                    (2114)   (31113)  (12115)
                    (2141)   (31131)  (12151)
                    (2411)   (31311)  (12511)
                    (4112)   (33111)  (15112)
                    (4121)            (15121)
                    (4211)            (15211)
                    (11222)           (21115)
                    (12122)           (21151)
                    (12212)           (21511)
                    (12221)           (25111)
                    (21122)           (51112)
                    (21212)           (51121)
                    (21221)           (51211)
                    (22112)           (52111)
                    (22121)
                    (22211)

Mathematica

Table[Length[Join@@Permutations/@Select[IntegerPartitions[n], Times@@#==n&]], {n, 0, 30}]

Crossrefs

The case of partitions is A001055.

Compositions are counted by A011782.

These compositions are ranked by A335404.

Cf. A003963, A096111, A124767, A233249, A272919, A301987, A301988, A333219, A333220, A331579.

Sequence in context: A092666 A019426 A333599 * A369924 A347800 A341738

Adjacent sequences: A335402 A335403 A335404 * A335406 A335407 A335408

Keyword

nonn

Author

Gus Wiseman, Jun 06 2020

Status

approved