John Conway <conway@Math.Princeton.EDU> wrote: ...

This raises the interesting question of whether every positive integer is the number of groups of some order? O'Beirne told me that Keith Devlin has worked on this, but I didn't get the impression he'd got very far.

I remember corresponding with Keith Dennis on that very question a few years ago. I contacted him after he submitted the sequence:

Most of my thinking has been on the universality question - "is every positive integer the number of groups of some order?". As I said, I'll report on that later. It gives rise to some more interesting sequences by the way, including 7,11,19,29,31,47,49,... .

A053403 in the EIS