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

1,2

Comments

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

Links

Table of n, a(n) for n=1..43.

Formula

Moebius transform is A032020 (strict compositions).

Example

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)

Mathematica

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

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.

Sequence in context: A058637 A026473 A272929 * A008319 A033311 A098504

Adjacent sequences: A336126 A336127 A336128 * A336130 A336131 A336132

Keyword

nonn

Author

Gus Wiseman, Jul 11 2020

Status

approved