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
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $6$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $6$