A100346 - OEIS

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

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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.