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 $1$, $4$, $9$, $16$, $25$, $36$, $\ldots$, $3249$, $3364$, $3481$, $3600$, $3721$, $3844$, $3969$:
- $4096 = 64 \times 64$
Also see
- Previous ... Next: Sixth Power
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Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $4096$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $4096$