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Version 4 |
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The first five $k$-multiperfect numbers for $1 < k < 6$ are small enough to fit on a single page without the aid of horizontal scrollbars, or breaking up the numbers into more than one lines. For $k > 5$, the numbers get quite big and writing them out becomes less practical. But since they tend to be divisible by lots of small primes, it makes sense to take advantage of the primorials. In the following table, the notation $n\#$ means the product of the first $n$ primes.
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The first five $k$-multiperfect numbers are small enough to fit on a single page, hopefully without the aid of horizontal scrollbars, or breaking up the numbers into more than one lines.
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| \begin{tabular}{|l|r|r|r|r|r|} |
\begin{tabular}{|l|r|r|r|r|r|} |
| 2 & 6 & 28 & 496 & 8128 & 33550336 \\ |
2 & 6 & 28 & 496 & 8128 & 33550336 \\ |
| 3 & 120 & 672 & 523776 & 459818240 & 1476304896 \\ |
3 & 120 & 672 & 523776 & 459818240 & 1476304896 \\ |
| 4 & 30240 & 32760 & 2178540 & 23569920 & 45532800 \\ |
4 & 30240 & 32760 & 2178540 & 23569920 & 45532800 \\ |
| 5 & 14182439040 & 31998395520 & 518666803200 & 13661860101120 & 30823866178560 \\ |
5 & 14182439040 & 31998395520 & 518666803200 & 13661860101120 & 30823866178560 \\ |
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6 & 154345556085770649600 & 9186050031556349952000 & $\frac{1}{3^{10} 5^{11} 7^{12} 11^{13}}(2310^{15} 3294623579)$ & $\frac{1}{5^7 7^8} (2^{19} 105^{10} 32728064417477)$ & $\displaystyle \frac{(13\#)2^{18} 105^5 793}{58339155}$ \\
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6 & 154345556085770649600 & 9186050031556349952000 & $\frac{1}{3^{10} 5^{11} 7^{12} 11^{13}}(2310^{15} 3294623579)$ & $\frac{1}{5^7 7^8} (2^{19} 105^{10} 32728064417477)$ & $\frac{13}{49} (2^{19} 105^5 7490143456939)$ \\
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| \end{tabular} |
\end{tabular} |
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| The smallest 7-multiperfect number is 141310897947438348259849402738485523264343544818565120000. |
The smallest 7-multiperfect number is 141310897947438348259849402738485523264343544818565120000. |
