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A100346 Number of compositions of n into divisors of n.

%I A100346 #18 Nov 08 2023 10:32:20
%S A100346 1,1,2,2,6,2,25,2,56,20,129,2,1628,2,742,450,5272,2,45316,2,83344,
%T A100346 3321,29967,2,5105722,572,200390,26426,5469759,2,154004511,2,47350056,
%U A100346 226020,9262157,51886,15140335650,2,63346598,2044895,14700095926,2,185493291001,2
%N A100346 Number of compositions of n into divisors of n.
%H A100346 Alois P. Heinz, <a href="/A100346/b100346.txt">Table of n, a(n) for n = 0..2000</a>
%F A100346 Coefficient of x^n in expansion of 1/(1-Sum_{d divides n} x^d ).
%p A100346 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
%p A100346 # second Maple program:
%p A100346 a:= proc(n) option remember; local b, l;
%p A100346       l, b:= numtheory[divisors](n),
%p A100346       proc(m) option remember; `if`(m=0, 1,
%p A100346          add(`if`(j>m, 0, b(m-j)), j=l))
%p A100346       end; b(n)
%p A100346     end:
%p A100346 seq(a(n), n=0..50);  # _Alois P. Heinz_, Mar 28 2017
%t A100346 a[n_] := SeriesCoefficient[1/(1-DivisorSum[n, x^#&]), {x, 0, n}]; Array[a, 50] (* _Jean-François Alcover_, Apr 06 2017 *)
%Y A100346 Cf. A018818.
%K A100346 easy,nonn
%O A100346 0,3
%A A100346 _Vladeta Jovovic_, Dec 29 2004
%E A100346 More terms from _Emeric Deutsch_, Feb 16 2005
%E A100346 a(0)=1 prepended by _Alois P. Heinz_, Nov 08 2023