Smallest Multiply Perfect Number of Order 6

Theorem

The number $154 \, 345 \, 556 \, 085 \, 770 \, 649 \, 600$ is multiply perfect of order $6$:

\(\ds \map {\sigma_1} {154 \, 345 \, 556 \, 085 \, 770 \, 649 \, 600}\)

\(=\)

\(\ds 926 \, 073 \, 336 \, 514 \, 623 \, 897 \, 600\)

\(\ds \)

\(=\)

\(\ds 6 \times 154 \, 345 \, 556 \, 085 \, 770 \, 649 \, 600\)

It is the smallest positive integer to be so.

Proof

From $\sigma_1$ of $154 \, 345 \, 556 \, 085 \, 770 \, 649 \, 600$:

$\map {\sigma_1} {154 \, 345 \, 556 \, 085 \, 770 \, 649 \, 600} = 926 \, 073 \, 336 \, 514 \, 623 \, 897 \, 600$

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Sources

• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $154,345,556,085,770,649,600$