27,418, 521,963, 671,501, 273,905, 190,135, 082,692, 041,730, 405,303, 870,249, 023,209
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Number
$27 \, 418 \, 521 \, 963 \, 671 \, 501 \, 273 \, 905 \, 190 \, 135 \, 082 \, 692 \, 041 \, 730 \, 405 \, 303 \, 870 \, 249 \, 023 \, 209$ is:
- $3^9 \times 7^3 \times 11^3 \times 13^3 \times 17^3 \times 41^3 \times 43^3 \times 47^3 \times 443^3 \times 499^3 \times 3583^3$
- The $30 \, 154 \, 214 \, 043 \, 975 \, 990 \, 969$th cube number:
- $27 \, 418 \, 521 \, 963 \, 671 \, 501 \, 273 \, 905 \, 190 \, 135 \, 082 \, 692 \, 041 \, 730 \, 405 \, 303 \, 870 \, 249 \, 023 \, 209 = 30 \, 154 \, 214 \, 043 \, 975 \, 990 \, 969^3$
- The smallest cube $N$ whose such that the divisor sum of $N$ is also a cube:
| \(\ds \qquad\) | \(\) | \(\ds \map {\sigma_1} {27 \, 418 \, 521 \, 963 \, 671 \, 501 \, 273 \, 905 \, 190 \, 135 \, 082 \, 692 \, 041 \, 730 \, 405 \, 303 \, 870 \, 249 \, 023 \, 209}\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 65 \, 400 \, 948 \, 817 \, 364 \, 742 \, 403 \, 487 \, 616 \, 930 \, 512 \, 213 \, 536 \, 407 \, 552 \, 000 \, 000 \, 000 \, 000 \, 000\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 2^{39} \times 3^6 \times 5^{15} \times 7^3 \times 11^3 \times 13^3 \times 17^3 \times 29^3 \times 37^3 \times 61^3 \times 157^3\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 40 \, 289 \, 760 \, 243 \, 532 \, 800 \, 000^3\) |
Arithmetic Functions on $27 \, 418 \, 521 \, 963 \, 671 \, 501 \, 273 \, 905 \, 190 \, 135 \, 082 \, 692 \, 041 \, 730 \, 405 \, 303 \, 870 \, 249 \, 023 \, 209$
| \(\ds \map {\sigma_1} { 27 \, 418 \, 521 \, 963 \, 671 \, 501 \, 273 \, 905 \, 190 \, 135 \, 082 \, 692 \, 041 \, 730 \, 405 \, 303 \, 870 \, 249 \, 023 \, 209 }\) | \(=\) | \(\ds 65 \, 400 \, 948 \, 817 \, 364 \, 742 \, 403 \, 487 \, 616 \, 930 \, 512 \, 213 \, 536 \, 407 \, 552 \, 000 \, 000 \, 000 \, 000 \, 000\) | $\sigma_1$ of $27 \, 418 \, 521 \, 963 \, 671 \, 501 \, 273 \, 905 \, 190 \, 135 \, 082 \, 692 \, 041 \, 730 \, 405 \, 303 \, 870 \, 249 \, 023 \, 209$ |
Also see
- Previous ... Next: Cube Number
Sources
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $3^9 7^3 11^3 13^3 17^3 41^3 43^3 47^3 443^3 499^3 3583^3$