The largest S-smooth subset of [1,X] without a forbidden configuration {n, p1 n, ..., pr n} has size r/(r+1) times the total count of S-smooth numbers plus an error of size (log X)^{r-1}.
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Extremal densities for forbidden configurations in $S$-smooth numbers
The largest S-smooth subset of [1,X] without a forbidden configuration {n, p1 n, ..., pr n} has size r/(r+1) times the total count of S-smooth numbers plus an error of size (log X)^{r-1}.