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 $220$:
- $\map {\sigma_1} {220} = \map {\sigma_1} {284} = 504 = 220 + 284$
- 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 $\map {\sigma_1} n = \map {\sigma_1} {n + 2}$ after $33, 54$:
- $\map {\sigma_1} {284} = 504 = \map {\sigma_1} {286}$
- 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 $284$
\(\ds \map {\sigma_1} { 284 }\) | \(=\) | \(\ds 504\) | $\sigma_1$ of $284$ |
Also see
- Previous ... Next: Amicable Pair
- Previous ... Next: Thabit Pair
- Previous ... Next: Nontotient
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $220$
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $284$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $220$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $284$