Smallest Multiply Perfect Number of Order 5

Theorem

The number $14 \, 182 \, 439 \, 040$ is multiply perfect of order $5$:

$\map {\sigma_1} {14 \, 182 \, 439 \, 040} = 70 \, 912 \, 195 \, 200 = 5 \times 14 \, 182 \, 439 \, 040$

It is the smallest positive integer to be so.

Proof

From $\sigma_1$ of $14 \, 182 \, 439 \, 040$:

$\map {\sigma_1} {14 \, 182 \, 439 \, 040} = 70 \, 912 \, 195 \, 200$

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Sources

• 1994: Richard K. Guy: Unsolved Problems in Number Theory (2nd ed.)

• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $14,182,439,040$