Square whose Divisor Sum is Cubic
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Theorem
The number $1 \, 857 \, 437 \, 604$ is a square number whose divisor sum is a cube.
Proof
| \(\ds 1 \, 857 \, 437 \, 604\) | \(=\) | \(\ds 43 \, 098^2\) | ||||||||||||
| \(\ds \map {\sigma_1} {1 \, 857 \, 437 \, 604}\) | \(=\) | \(\ds 5 \, 168 \, 743 \, 489\) | $\sigma_1$ of $1 \, 857 \, 437 \, 604$ | |||||||||||
| \(\ds \) | \(=\) | \(\ds 1729^3\) |
$\blacksquare$
Sources
- 1964: Albert H. Beiler: Recreations in the Theory of Numbers
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $1,857,437,604$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $1,857,437,604$