Related to : How to approximate the number of groups?
Here :
https://groupprops.subwiki.org/wiki/Number_of_groups_of_given_order
an inequality is mentioned which can be written as $$gnu(ab)\ge gnu(a)\cdot gnu(b)$$ where $\ gnu(n)\ $ denotes the number of groups of order $\ n\ $ upto isomorphism.
It is explicitely stated that $\ a\ $ and $\ b\ $ have to be coprime. So, I wondered for which positive integers $a,b$ the inequality does NOT hold.
To check this, I used $\ gnu(n)\ $ for $\ n\le 2047\ $ : whenever $ab\le 2047$, the inequality is satisfied.
Can we omit that $a$ and $b$ are coprime ? If not, what else is necessary ?