284

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

Also see