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

0,5

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)

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 *)

Prog

(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

Crossrefs

Cf. A065205, A211110, A018818.

Sequence in context: A063754 A163117 A099749 * A077202 A086665 A273013

Adjacent sequences: A210439 A210440 A210441 * A210443 A210444 A210445

Keyword

nonn,look

Author

Reinhard Zumkeller, Jan 21 2013

Status

approved