Perhaps the question should be stated more clearly.
When is A000799(n) = A064355(n) ?
I get differences A000799(n) - A064355(n):
[0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,0,0,3,0,0,6,0,0,10,1,0,18,0,0,36,0,0,62,0,
...]
> Do you mean the equality
> 1/n * sum_{d divides n and d is odd} 2^(n/d) * mu(d) = floor( 2^n /n )
?
>
> How to prove it?