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A210442 Number of partitions of n into proper divisors of n, cf. A027751. 7
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

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

LINKS

Reinhard Zumkeller and 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-Fran├žois 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

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Last modified October 19 04:40 EDT 2019. Contains 328211 sequences. (Running on oeis4.)