3136

From ProofWiki
Jump to navigation Jump to search

Previous  ... Next

Number

$3136$ (three thousand, one hundred and thirty-six) is:

$2^6 \times 7^2$


The $21$st square number after $1$, $4$, $36$, $121$, $144$, $256$, $\ldots$, $1936$, $2304$, $2704$, $2916$ to be the divisor sum value of some (strictly) positive integer:
$3136 = \map {\sigma_1} {1092} = \map {\sigma_1} {1612} = \map {\sigma_1} {2037} = \map {\sigma_1} {2899} = \map {\sigma_1} {3007}$


The $46$th positive integer which cannot be expressed as the sum of a square and a prime:
$1$, $10$, $25$, $34$, $58$, $64$, $85$, $\ldots$, $2209$, $2304$, $2500$, $2809$, $2986$, $3136$, $\ldots$


The $56$th square number after $1$, $4$, $9$, $16$, $25$, $36$, $\ldots$, $1936$, $2025$, $2116$, $2209$, $2304$, $2401$, $2500$, $2601$, $2704$, $2809$, $2916$, $3025$:
$3136 = 56 \times 56$


Also see