# 4096

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## Number

$4096$ (four thousand and ninety-six) is:

$2^{12}$
Hence in binary notation:
$1 \, 000 \, 000 \, 000 \, 000$

The $3$rd power of $16$ after $(1)$, $16$, $256$:
$4096 = 16^3$

The $4$th $6$th power after $1$, $64$, $729$:
$4096 = 4 \times 4 \times 4 \times 4 \times 4 \times 4$

The $4$th power of $8$ after $(1)$, $8$, $64$, $512$:
$4096 = 8^4$

The $6$th power of $4$ after $(1)$, $4$, $16$, $64$, $256$, $1024$:
$4096 = 4^6$

The $8$th fourth power after $1$, $16$, $81$, $256$, $625$, $1296$, $2401$:
$4096 = 8 \times 8 \times 8 \times 8$
Hence in octal notation:
$10 \, 000$

The $12$th power of $2$ after $(1)$, $2$, $4$, $8$, $16$, $32$, $64$, $128$, $256$, $512$, $1024$, $2048$:
$4096 = 2^{12}$

The $13$th almost perfect number after $1$, $2$, $4$, $8$, $16$, $32$, $64$, $128$, $256$, $512$, $1024$, $2048$:
$\map {\sigma_1} {4096} = 8191 = 2 \times 4096 - 1$

The $16$th cube number after $1$, $8$, $27$, $64$, $125$, $216$, $343$, $512$, $729$, $1000$, $1331$, $1728$, $2197$, $2744$, $3375$:
$4096 = 16 \times 16 \times 16$
Hence in hexadecimal notation:
$1000$

The $24$th square number after $1$, $4$, $36$, $121$, $144$, $256$, $\ldots$, $1936$, $2304$, $2704$, $2916$, $3136$, $3600$, $3844$ to be the divisor sum value of some (strictly) positive integer:
$4096 = \map {\sigma_1} {2667} = \map {\sigma_1} {3937}$

The $64$th square number after $1$, $4$, $9$, $16$, $25$, $36$, $\ldots$, $3249$, $3364$, $3481$, $3600$, $3721$, $3844$, $3969$:
$4096 = 64 \times 64$