Perfection quotient
= Perfection quotient
{title2=$\sigma(n)/n$}
The ratio of the sum of the positive <divisors> of a <positive integer> to that <integer>. For <coprime> $a,b$, the ratio is multiplicative because the <divisor function> $\sigma$ is multiplicative. The contribution of a <prime power> $p^e$ is $(1+p+\cdots+p^e)/p^e$, so a prescribed quotient can be searched through its remaining <numerator> and <denominator>.