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A338943 a(n) is the least number k such that the average number of distinct prime divisors of {1..k} is >= n.

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%I A338943 #21 Feb 16 2025 08:34:01
%S A338943 1,6,455,8167302
%N A338943 a(n) is the least number k such that the average number of distinct prime divisors of {1..k} is >= n.
%C A338943 10^18 < a(4) < 10^19. - _Daniel Suteu_, Nov 17 2020
%H A338943 Chris K. Caldwell and G. L. Honaker, Jr., <a href="https://primes.utm.edu/curios/page.php?curio_id=33972">Prime Curio for 455</a>
%H A338943 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DistinctPrimeFactors.html">Distinct Prime Factors</a>.
%e A338943 a(2) = 455 because the average number of distinct prime divisors of {1..455} is >= 2.
%Y A338943 Cf. A001221, A013939, A085829, A328331, A338891.
%K A338943 nonn,more
%O A338943 0,2
%A A338943 _Ilya Gutkovskiy_, Nov 17 2020