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

Author

Gus Wiseman, Jun 06 2020

Keywords

• nonn

Comments

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

Examples

			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)
		

Links

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

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.

Programs

Mathematica

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