Definition:Hardy-Ramanujan Number/Examples
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Examples of Hardy-Ramanujan Numbers
$1729$: Hardy-Ramanujan Number $\operatorname{Ta} \left({2}\right)$
The $2$nd Hardy-Ramanujan number $\map {\operatorname {Ta}} 2$ is $1729$:
| \(\ds 1729\) | \(=\) | \(\ds 12^3 + 1^3\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 10^3 + 9^3\) |
$87 \, 539 \, 319$: Hardy-Ramanujan Number $\operatorname{Ta} \left({3}\right)$
The $3$rd Hardy-Ramanujan number $\map {\mathrm {Ta} } 3$ is $87 \, 539 \, 319$:
| \(\ds 87 \, 539 \, 319\) | \(=\) | \(\ds 167^3 + 436^3\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 228^3 + 423^3\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 255^3 + 414^3\) |
$6 \, 963 \, 472 \, 309 \, 248$: Hardy-Ramanujan Number $\operatorname{Ta} \left({4}\right)$
The $4$th Hardy-Ramanujan number $\operatorname {Ta} \left({4}\right)$ is $6 \, 963 \, 472 \, 309 \, 248$:
| \(\ds 6 \, 963 \, 472 \, 309 \, 248\) | \(=\) | \(\ds 2421^3 + 19 \, 083^3\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 5436^3 + 18 \, 948^3\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 10 \, 200^3 + 18 \, 072^3\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 13 \, 322^3 + 16 \, 630^3\) |