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We find the formula for the cardinality of maximal set of integers from $[1,\ldots,n]$ which does not contain $k+1$ pairwise coprimes and has divisors from a specified set of primes. This formula is defined by the set of multiples of the generating set, which does not depend on $n$.

Maximal sets of integers not containing $k+1$ pairwise coprimes and having divisors from a specified set of primes