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%I #15 Jul 28 2015 14:03:56
%S 0,0,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,3,0,2,0,0,0,7,0,0,0,0,0,6,0,0,0,0,
%T 0,8,0,0,0,6,0,5,0,0,0,0,0,9,0,0,0,0,0,5,0,5,0,0,0,11,0,0,0,0,0,5,0,0,
%U 0,2,0,11,0,0,0,0,0,4,0,8,0,0,0,11,0,0,0,3,0,11,0,0,0,0,0,11,0,0,0,5
%N Number of divisors of n that do not exceed the abundance of n.
%C a(n) = #{d>0: d <= A033880(n) and n mod d = 0};
%C a(A005101(n))>0, a(A000396(n))=a(A005100(n))=0.
%H Matthew House, <a href="/A089371/b089371.txt">Table of n, a(n) for n = 1..10000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Abundance.html">Abundance</a>
%p f:= proc(n) local r;
%p r:= numtheory:-sigma(n) - 2*n;
%p if r <= 0 then 0
%p else nops(select(`<=`,numtheory:-divisors(n),r))
%p fi
%p end proc:
%p map(f, [$1..100]); # _Robert Israel_, Jul 27 2015
%t Table[Count[Divisors@ n, x_ /; x <= DivisorSigma[1, n] - 2 n], {n,
%t 120}] (* _Michael De Vlieger_, Jul 27 2015 *)
%o (PARI) a(n) = my(ab = sigma(n) - 2*n); sumdiv(n, d, d <= ab); \\ _Michel Marcus_, Jul 27 2015
%Y Cf. A000005, A000203, A000396, A001065, A005100, A005101, A033880.
%K nonn
%O 1,12
%A _Reinhard Zumkeller_, Dec 27 2003
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