1024

Number
$1024$ (one thousand and twenty-four) is:
 * $2^{10}$


 * The $1$st number with at least $10$ prime factors:
 * $1024 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2$


 * The $4$th fifth power after $1$, $32$, $243$:
 * $1024 = 4 \times 4 \times 4 \times 4 \times 4$


 * The $5$th power of $4$ after $(1)$, $4$, $16$, $64$, $256$:
 * $1024 = 4^5$


 * The $10$th power of $2$ after $(1)$, $2$, $4$, $8$, $16$, $32$, $64$, $128$, $256$, $512$:
 * $1024 = 2^{10}$


 * The $11$th almost perfect number after $1$, $2$, $4$, $8$, $16$, $32$, $64$, $128$, $256$, $512$:
 * $\map \sigma {1024} = 2047 = 2 \times 1024 - 1$


 * The $13$th square number after $1$, $4$, $36$, $121$, $144$, $256$, $324$, $400$, $576$, $784$, $900$, $961$ to be the $\sigma$ (sigma) value of some (strictly) positive integer:
 * $1024 = \map \sigma {651} = \map \sigma {889}$


 * The $28$th positive integer which cannot be expressed as the sum of a square and a prime:
 * $1$, $10$, $25$, $34$, $58$, $64$, $85$, $\ldots$, $400$, $526$, $529$, $625$, $676$, $706$, $730$, $771$, $784$, $841$, $1024$, $\ldots$


 * The $32$nd square number after $1$, $4$, $9$, $16$, $25$, $36$, $\ldots$, $625$, $676$, $729$, $784$, $841$, $900$, $961$:
 * $1024 = 32 \times 32$

Also see