Square whose Divisor Sum is Cubic

Theorem

The number $1 \, 857 \, 437 \, 604$ is a square number whose divisor sum is a cube.

$\ds 1 \, 857 \, 437 \, 604$

$=$

$\ds 43 \, 098^2$

$\ds \map {\sigma_1} {1 \, 857 \, 437 \, 604}$

$=$

$\ds 5 \, 168 \, 743 \, 489$

$\ds $

$=$

$\ds 1729^3$

$\blacksquare$

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): $1,857,437,604$