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

0,3

Links

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

Formula

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

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 *)

Crossrefs

Cf. A018818.

Sequence in context: A130674 A284839 A286376 * A359004 A306387 A308692

Adjacent sequences: A100343 A100344 A100345 * A100347 A100348 A100349

Keyword

easy,nonn

Author

Vladeta Jovovic, Dec 29 2004

Extensions

More terms from Emeric Deutsch, Feb 16 2005

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

Status

approved