A331979 Number of compositions (ordered partitions) of n into distinct nontrivial divisors of n.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 30, 0, 0, 0, 0, 0, 30, 0, 0, 0, 0, 0, 894, 0, 0, 0, 24, 0, 6, 0, 0, 0, 0, 0, 894, 0, 0, 0, 0, 0, 30, 0, 120, 0, 0, 0, 19518, 0, 0, 0, 0, 0, 126, 0, 0, 0, 0, 0, 18558, 0, 0, 0, 0, 0, 6, 0, 864

Offset: 0

Author

Ilya Gutkovskiy, Feb 03 2020

Keywords

• nonn

Examples

			a(12) = 6 because we have [6, 4, 2], [6, 2, 4], [4, 6, 2], [4, 2, 6], [2, 6, 4] and [2, 4, 6].
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000
• Index entries for sequences related to compositions

Crossrefs

Cf. A018818, A027750, A033630, A065205, A070824, A100346, A211111, A293813, A293814, A294137, A294138, A331927, A331928.

Programs

Maple

with(numtheory):
a:= proc(n) local b, l; l:= sort([(divisors(n) minus {1, n})[]]):
      b:= proc(m, i, p) option remember; `if`(m=0, p!, `if`(i<1, 0,
             b(m, i-1, p)+`if`(l[i]>m, 0, b(m-l[i], i-1, p+1))))
          end; forget(b):
      b(n, nops(l), 0)
    end:
seq(a(n), n=0..100);  # Alois P. Heinz, Feb 03 2020

Mathematica

a[n_] := If[n == 0, 1, Module[{b, l = Divisors[n] ~Complement~ {1, n}}, b[m_, i_, p_] := b[m, i, p] = If[m == 0, p!, If[i < 1, 0, b[m, i-1, p] + If[l[[i]] > m, 0, b[m - l[[i]], i-1, p+1]]]]; b[n, Length[l], 0]]];
a /@ Range[0, 100] (* Jean-François Alcover, Nov 17 2020, after Alois P. Heinz *)