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How many finite loops of order $n$ are there?

I interested in the exact values ​​of $n$ if $n <40$.

  I also interested in formulae or bounds for all $n$.

How many finite loops of order $n$ are there?

I am interested in the exact values ​​of $n$ if $n <40$ or even reasonable estimates. I am also interested in formulae or bounds for all $n$.

Note that similar questions have been studied for groups and semigroups. Much information is available in the group theory case, but even for semigroups not much is known beyond $n=11$.

How many finite loops of order $n$ are there? I interested in the exact values ​​of $n$ if $n <40$? I also interested in formulae or bounds for all $n$. I was particularly interested in loops, have the additional property of associativity some analogs.

How many finite loops of order $n$ are there?

I interested in the exact values ​​of $n$ if $n <40$.

I also interested in formulae or bounds for all $n$.

How many finite loops of order $n$ are there? I interested in the exact values ​​of n if n <40? I also interested in formulae or bounds for all n. I was particularly interested in loops, have the additional property of associativity some analogs.

How many finite loops of order $n$ are there? I interested in the exact values ​​of $n$ if $n <40$? I also interested in formulae or bounds for all $n$. I was particularly interested in loops, have the additional property of associativity some analogs.