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A089371
Number of divisors of n that do not exceed the abundance of n.
1
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, 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, 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
OFFSET
1,12
COMMENTS
a(n) = #{d>0: d <= A033880(n) and n mod d = 0};
a(A005101(n))>0, a(A000396(n))=a(A005100(n))=0.
LINKS
Eric Weisstein's World of Mathematics, Abundance
MAPLE
f:= proc(n) local r;
r:= numtheory:-sigma(n) - 2*n;
if r <= 0 then 0
else nops(select(`<=`, numtheory:-divisors(n), r))
fi
end proc:
map(f, [$1..100]); # Robert Israel, Jul 27 2015
MATHEMATICA
Table[Count[Divisors@ n, x_ /; x <= DivisorSigma[1, n] - 2 n], {n,
120}] (* Michael De Vlieger, Jul 27 2015 *)
PROG
(PARI) a(n) = my(ab = sigma(n) - 2*n); sumdiv(n, d, d <= ab); \\ Michel Marcus, Jul 27 2015
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Dec 27 2003
STATUS
approved