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A089371
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Number of divisors of n that do not exceed the abundance of n.
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1
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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
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OFFSET
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1,12
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COMMENTS
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a(n) = #{d>0: d <= A033880(n) and n mod d = 0};
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LINKS
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Eric Weisstein's World of Mathematics, Abundance
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MAPLE
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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:
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MATHEMATICA
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Table[Count[Divisors@ n, x_ /; x <= DivisorSigma[1, n] - 2 n], {n,
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PROG
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(PARI) a(n) = my(ab = sigma(n) - 2*n); sumdiv(n, d, d <= ab); \\ Michel Marcus, Jul 27 2015
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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