A100346 Number of compositions of n into divisors of n.

1, 1, 2, 2, 6, 2, 25, 2, 56, 20, 129, 2, 1628, 2, 742, 450, 5272, 2, 45316, 2, 83344, 3321, 29967, 2, 5105722, 572, 200390, 26426, 5469759, 2, 154004511, 2, 47350056, 226020, 9262157, 51886, 15140335650, 2, 63346598, 2044895, 14700095926, 2, 185493291001, 2

Offset: 0

Author

Vladeta Jovovic, Dec 29 2004

Keywords

• easy
• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..2000

Crossrefs

Cf. A018818.

Programs

Maple

with(numtheory): G:=proc(n) local DV: DV:=divisors(n): 1/(1-sum(x^DV[j], j=1..tau(n))) end: seq(coeff(series(G(n), x, 80), x, n), n=0..44); # Emeric Deutsch, Feb 16 2005
# second Maple program:
a:= proc(n) option remember; local b, l;
      l, b:= numtheory[divisors](n),
      proc(m) option remember; `if`(m=0, 1,
         add(`if`(j>m, 0, b(m-j)), j=l))
      end; b(n)
    end:
seq(a(n), n=0..50);  # Alois P. Heinz, Mar 28 2017

Mathematica

a[n_] := SeriesCoefficient[1/(1-DivisorSum[n, x^#&]), {x, 0, n}]; Array[a, 50] (* Jean-François Alcover, Apr 06 2017 *)

Formula

Coefficient of x^n in expansion of 1/(1-Sum_{d divides n} x^d ).

Extensions

More terms from Emeric Deutsch, Feb 16 2005

a(0)=1 prepended by Alois P. Heinz, Nov 08 2023