# 284

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## Number

$284$ (two hundred and eighty-four) is:

$2^2 \times 71$

The larger of the $1$st amicable pair, with $220$:
$\map \sigma {220} = \map \sigma {284} = 504 = 220 + 284$
which is also the first Thabit pair:
$220 = 2^2 \times 11 \times 5 = 2^2 \paren {3 \times 2^2 - 1} \paren {3 \times 2^{2 - 1} - 1}, 284 = 2^2 \paren {9 \times 2^{2 \times 2 - 1} - 1}$

The $3$rd integer solution to $\map \sigma n = \map \sigma {n + 2}$ after $33, 54$:
$\map \sigma {284} = 504 = \map \sigma {286}$

The $45$th nontotient:
$\nexists m \in \Z_{>0}: \map \phi m = 284$
where $\map \phi m$ denotes the Euler $\phi$ function

### Arithmetic Functions on $284$

 $\ds \map \sigma { 284 }$ $=$ $\ds 504$ $\sigma$ of $284$