Only Number which is Sum of 3 Factors is 6/Mistake

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Source Work

1986: David Wells: Curious and Interesting Numbers:

The Dictionary
$6$


1997: David Wells: Curious and Interesting Numbers (2nd ed.):

The Dictionary
$6$


Mistake

It is the only number that is the sum of exactly $3$ of its factors, ...


Correction

The statement should be:

It is the only number that is the sum of exactly $3$ of its distinct coprime factors, ...


Let $n$ be such a positive integer with corresponding divisors $a, b, c$ such that:

$a + b + c = n$

We note that the set $\set {k a, k b, k c}$ satisfy the same properties trivially as divisors of $k n$.

Hence it is necessary definitely to require the set to be coprime.


Also note the trivial observation that $1 + 1 + 1 = 3$, which explains the need to specify that the factors be distinct.


Sources