Weird Number/Examples/70
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Example of a Weird Number
$70$ is a weird number:
The aliquot sum of $70$ is $74$, but no subset of its aliquot parts add to $70$.
Proof
From $\sigma_1$ of $70$:
- $\map {\sigma_1} {70} = 144$
where $\sigma_1$ denotes the divisor sum.
The aliquot sum of $70$ is given by:
- $\map {\sigma_1} {70} - 70 = 144 - 70 = 74$
The aliquot parts of $70$ are:
- $1, 2, 5, 7, 10, 14, 35$
Note that $4$ is not an aliquot part of $70$.
Thus $70 = 74 - 4$ cannot be made by any combination of those aliquot parts.
Hence the result.
$\blacksquare$
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $70$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $70$