784

Number
$784$ (seven hundred and eighty-four) is:
 * $2^4 \times 7^2$


 * The $10$th square number after $1$, $4$, $36$, $121$, $144$, $256$, $324$, $400$, $576$ to be the $\sigma$ (sigma) value of some (strictly) positive integer:
 * $784 = \map \sigma {364}$


 * The $28$th square number after $1$, $4$, $9$, $16$, $25$, $36$, $\ldots$, $361$, $400$, $441$, $484$, $529$, $57$, $625$, $676$, $729$:
 * $784 = 28 \times 28$


 * The $47$th powerful number after $1$, $4$, $8$, $9$, $16$, $25$, $\ldots$, $400$, $432$, $441$, $484$, $500$, $512$, $529$, $576$, $625$, $648$, $675$, $676$, $729$:
 * $784 = 2^4 \times 7^2$


 * The $12$th even integer after $2$, $4$, $94$, $96$, $98$, $400$, $402$, $404$, $514$, $516$, $518$ that cannot be expressed as the sum of $2$ prime numbers which are each one of a pair of twin primes


 * The $26$th positive integer which cannot be expressed as the sum of a square and a prime:
 * $1$, $10$, $25$, $34$, $58$, $64$, $85$, $91$, $121$, $130$, $169$, $196$, $214$, $226$, $289$, $324$, $370$, $400$, $526$, $529$, $625$, $676$, $706$, $730$, $771$, $784$, $\ldots$


 * The sum of the first $7$ cubes:
 * $784 = 1^3 + 2^3 + 3^3 + 4^3 + 5^3 + 6^3 + 7^3$