220

Number
$220$ (two hundred and twenty) is:


 * $2^2 \times 5 \times 11$


 * The $10$th tetrahedral number, after $1, 4, 10, 20, 35, 56, 84, 120, 165$:
 * $165 = 1 + 3 + 6 + 10 + 15 + 21 + 28 + 36 + 45 + 55 = \dfrac {10 \left({10 + 1}\right) \left({10 + 2}\right)} 6$


 * The smaller of the $1$st amicable pair, with $284$:
 * $\sigma \left({220}\right) = \sigma \left({284}\right) = 504 = 220 + 284$


 * which is also the first Thabit pair:
 * $220 = 2^2 \times 11 \times 5 = 2^2 \left({3 \times 2^2 - 1}\right) \left({3 \times 2^{2 - 1} - 1}\right), 224 = 2^2 \left({9 \times 2^{2 \times 2 - 1} - 1}\right)$