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: Integers Differing by 2 with Same Divisor Sum

• 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): $284$