A014648 Number of partitions of n into its divisors with at least one part of size 1.

1, 1, 1, 2, 1, 5, 1, 6, 3, 8, 1, 33, 1, 11, 11, 26, 1, 66, 1, 76, 15, 17, 1, 378, 5, 20, 18, 136, 1, 648, 1, 166, 23, 26, 23, 1954, 1, 29, 27, 1212, 1, 1500, 1, 309, 261, 35, 1, 8600, 7, 378, 35, 422, 1, 2877, 35, 2803, 39, 44, 1, 66129, 1, 47, 461, 1626, 41, 4936

Offset

1,4

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Formula

Coefficient of x^(n-1) in expansion of 1/Product_{d divides n} (1-x^d). - Vladeta Jovovic, Apr 11 2004

Maple

with(numtheory):
a:= proc(n) option remember; local b, l; l:= sort([divisors(n)[]]):
      b:= proc(m, i) option remember; `if`(m=0, 1, `if`(i<1, 0,
             b(m, i-1)+`if`(l[i]>m, 0, b(m-l[i], i))))
          end; forget(b):
      b(n-1, nops(l))
    end:
seq(a(n), n=1..100); # Alois P. Heinz, Feb 05 2014

Mathematica

a[n_] := a[n] = Module[{b, l}, l = Divisors[n]; b[m_, i_] := b[m, i] = If[m==0, 1, If[i<1, 0, b[m, i-1] + If[l[[i]]>m, 0, b[m-l[[i]], i]]]]; b[n-1, Length[l]]]; Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Apr 07 2015, after Alois P. Heinz *)

Crossrefs

Cf. A018818.

Sequence in context: A347464 A249548 A014650 * A260147 A263454 A036073

Adjacent sequences: A014645 A014646 A014647 * A014649 A014650 A014651

Keyword

nonn

Author

Olivier Gérard

Status

approved