Only Number which is Sum of 3 Factors is 6

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Theorem

The only positive integer which is the sum of exactly $3$ of its divisors is $6$.


Corollary

$1$ can be expressed uniquely as the sum of $3$ distinct unit fractions:

$1 = \dfrac 1 2 + \dfrac 1 3 + \dfrac 1 6$


Proof


Sources