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For positive integers k, n let f(n, k) be the maximal cardinality of subsets of integers in the interval < 1, n > , which don’t have k + 1 pairwise coprimes. The set E(n, k) of integers in < 1, n > , which are divisible by one of the first k primes, certainly does not have k + 1 pairwise coprimes. Whereas we disproved in [1] an old conjecture of Erdös ([4], [5], [6], [7]) by showing that the equality (1) f(n, k) = |E(n, k)| does not always hold, we prove here that (1) holds for every k and all relative to k sufficiently large n .

Maximal sets of numbers not containing k+1 pairwise coprime integers