A336129 Number of strict compositions of divisors of n.

1, 2, 4, 5, 6, 16, 14, 24, 31, 64, 66, 120, 134, 208, 360, 459, 618, 894, 1178, 1622, 2768, 3364, 4758, 6432, 8767, 11440, 15634, 24526, 30462, 42296, 55742, 75334, 98112, 131428, 168444, 258403, 315974, 432244, 558464, 753132, 958266, 1280840, 1621274

Offset: 1

Author

Gus Wiseman, Jul 11 2020

Keywords

• nonn

Comments

A strict composition of k is a finite sequence of distinct positive integers summing to k.

Examples

			The a(1) = 1 through a(7) = 14 compositions:
  (1)  (1)  (1)    (1)    (1)    (1)      (1)
       (2)  (3)    (2)    (5)    (2)      (7)
            (1,2)  (4)    (1,4)  (3)      (1,6)
            (2,1)  (1,3)  (2,3)  (6)      (2,5)
                   (3,1)  (3,2)  (1,2)    (3,4)
                          (4,1)  (1,5)    (4,3)
                                 (2,1)    (5,2)
                                 (2,4)    (6,1)
                                 (4,2)    (1,2,4)
                                 (5,1)    (1,4,2)
                                 (1,2,3)  (2,1,4)
                                 (1,3,2)  (2,4,1)
                                 (2,1,3)  (4,1,2)
                                 (2,3,1)  (4,2,1)
                                 (3,1,2)
                                 (3,2,1)
		

Crossrefs

Compositions of divisors are A034729.

Strict partitions of divisors are A047966.

Partitions of divisors are A047968.

Cf. A000005, A001970, A006951, A133494, A318683, A336128, A336130, A336132.

Programs

Mathematica

Table[Sum[Length[Join@@Permutations/@Select[IntegerPartitions[d],UnsameQ@@#&]],{d,Divisors[n]}],{n,12}]

Formula

Moebius transform is A032020 (strict compositions).