Even Integer with Abundancy Index greater than 9/Mistake

Source Work

1997: David Wells: Curious and Interesting Numbers (2nd ed.):

The Dictionary

$55$

Mistake

Every even number $n$ whose abundancy index, defined to equal $\map \sigma n / n$, is greater than $9$, has at least $55$ distinct prime factors.

Correction

The author appears to have confused the numbers of distinct prime factors for abundancy indices over $9$ and $10$.

The correct statements are:

Every even number $n$ whose abundancy index ... is greater than $9$, has at least $35$ distinct prime factors

and:

Every even number $n$ whose abundancy index ... is greater than $10$, has at least $55$ distinct prime factors.

Sources

• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $55$