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