A210442 Number of partitions of n into proper divisors of n, cf. A027751.

1, 0, 1, 1, 3, 1, 7, 1, 9, 4, 10, 1, 44, 1, 13, 13, 35, 1, 80, 1, 91, 17, 19, 1, 457, 6, 22, 22, 155, 1, 741, 1, 201, 25, 28, 25, 2233, 1, 31, 29, 1369, 1, 1653, 1, 336, 285, 37, 1, 9675, 8, 406, 37, 453, 1, 3131, 37, 3064, 41, 46, 1, 73154, 1, 49, 492, 1827

Offset: 0

Author

Reinhard Zumkeller, Jan 21 2013

Keywords

• nonn
• look

Comments

For n > 0: a(A000040(n)) = 1 and a(A002808(n)) > 1.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000 (terms n = 0..197 from Reinhard Zumkeller)

Crossrefs

Cf. A065205, A211110, A018818.

Programs

Haskell

a210442 n = p (a027751_row n) n where
   p _          0 = 1
   p []         _ = 0
   p ks'@(k:ks) m = if m < k then 0 else p ks' (m - k) + p ks m

Maple

with(numtheory):
a:= proc(n) local b, l; l:= sort([(divisors(n) minus {n})[]]):
      b:= proc(m, i) option remember; `if`(m=0 or i=1, 1,
            `if`(i<1, 0, b(m, i-1)+`if`(l[i]>m, 0, b(m-l[i], i))))
          end; forget(b):
      b(n, nops(l))
    end:
seq(a(n), n=0..100); # Alois P. Heinz, Jan 29 2013

Mathematica

a[n_] := Module[{b, l}, l = Most[Divisors[n]]; b[m_, i_] := b[m, i] = If[m==0 || i==1, 1, If[i<1, 0, b[m, i-1] + If[l[[i]]>m, 0, b[m-l[[i]], i]]]]; b[n, Length[l]]]; a[0]=1; Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Feb 02 2017, after Alois P. Heinz *)