= Pretentious distance between one and the Möbius function
{title2=$D(1,\mu;X)\sim\sqrt{2\log\log X}$}
Because $\mu(p)=-1$, the squared <pretentious distance> from one to the <Möbius function> is twice the reciprocal-prime sum. The <Mertens second theorem> therefore gives $D(1,\mu;X)^2=2\log\log X+2B_1+o(1)$. In particular the distance diverges, illustrating that a multiplicative function can be far from the constant function even though both have unit-modulus <prime> values.
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