1024

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


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


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


 * The $11$th almost perfect number after $1, 2, 4, 8, 16, 32, 64, 128, 256, 512$:
 * $\sigma \left({1024}\right) = 2055 = 2 \times 1024 - 1$


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