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

0,13

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Index entries for sequences related to compositions

Example

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].

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 *)

Crossrefs

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

Sequence in context: A187794 A200214 A294887 * A005872 A035322 A270031

Adjacent sequences: A331976 A331977 A331978 * A331980 A331981 A331982

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 03 2020

Status

approved