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A080224
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Number of abundant divisors of n.
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21
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 3, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 4, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 5, 0, 0, 0, 0, 0, 1, 0, 3, 0, 0, 0, 3, 0, 0, 0, 1, 0, 3, 0, 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 1, 0, 1, 0
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OFFSET
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1,24
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COMMENTS
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Number of divisors d of n with sigma(d)>2*d (sigma = A000203)
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LINKS
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FORMULA
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(End)
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EXAMPLE
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Divisors of n=24: {1,2,3,4,6,8,12,24}, two of them are abundant: 12=A005101(1) and 24=A005101(4), therefore a(24)=2.
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MAPLE
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a := 0 ;
for d in numtheory[divisors](n) do
if numtheory[sigma](d) > 2*d then
a := a+1 ;
end if;
end do:
a;
end proc:
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MATHEMATICA
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Table[Count[Divisors[n], _?(DivisorSigma[1, #]>2#&)], {n, 110}] (* Harvey P. Dale, Jun 14 2013 *)
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PROG
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(PARI) a(n) = sumdiv(n, d, sigma(d)>2*d) \\ Michel Marcus, Mar 09 2013
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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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