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A014648 Number of partitions of n into its divisors with at least one part of size 1. 4
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 (list; graph; refs; listen; history; text; internal format)
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: A211361 A249548 A014650 * A260147 A263454 A036073

Adjacent sequences:  A014645 A014646 A014647 * A014649 A014650 A014651

KEYWORD

nonn

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified July 8 19:20 EDT 2020. Contains 335524 sequences. (Running on oeis4.)