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A210442 Number of partitions of n into proper divisors of n, cf. A027751. 10
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
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
Sequence in context: A063754 A163117 A099749 * A077202 A086665 A273013
KEYWORD
nonn,look
AUTHOR
Reinhard Zumkeller, Jan 21 2013
STATUS
approved

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Last modified June 23 12:51 EDT 2024. Contains 373648 sequences. (Running on oeis4.)