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A336129
Number of strict compositions of divisors of n.
0
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.
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.
Sequence in context: A058637 A026473 A272929 * A008319 A033311 A098504
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 11 2020
STATUS
approved