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Erdős problem 830

We say that a,bNa,b\in \mathbb{N} are an amicable pair if σ(a)=σ(b)=a+b\sigma(a)=\sigma(b)=a+b. If A(x)A(x) counts the number of amicable 1abx1\leq a\leq b\leq x then one can show that A(x)xexp((12+o(1))(logxloglogx)1/2)A(x) \leq x \exp(-(\tfrac{1}{2}+o(1))(\log x\log\log x)^{1/2}).

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