18,416

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Number

$18 \, 416$ (eighteen thousand, four hundred and sixteen) is:

$2^4 \times 1151$

The larger of the $8$th amicable pair, with $18 \, 416$:

$\map {\sigma_1} {17 \, 296} = \map {\sigma_1} {18 \, 416} = 35 \, 712 = 17 \, 296 + 18 \, 416$

which is also the $2$nd Thabit pair:

$17 \, 296 = 2^4 \times 23 \times 47 = 2^4 \paren {3 \times 2^4 - 1} \paren {3 \times 2^{3 - 1} - 1}, 18 \, 416 = 2^4 \paren {9 \times 2^{2 \times 4 - 1} - 1}$

Arithmetic Functions on $18 \, 416$

\(\ds \map {\sigma_1} { 18 \, 416 }\)

\(=\)

\(\ds 35 \, 712\)

$\sigma_1$ of $18 \, 416$

Also see

• Previous  ... Next: Amicable Pair
• Previous  ... Next: Thabit Pair

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $17,296$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $17,296$