jmc

Notice that inclusion of the integers from $34$ to $100$ is allowed as long as no integer between $11$ and $33$ inclusive is within the set. This provides a total of $100-34+1$ = 67 solutions. Further analyzation of the remaining integers between $1$ and $10$, we notice that we can include all the numbers except $3$ (as including $3$ would force us to remove both $9$ and $1$) to obtain the maximum number of $9$ solutions. Thus, $67+9=\boxed{76}$.