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a(n) is the least number k such that the average number of distinct prime divisors of {1..k} is >= n.
5

%I #20 Jun 13 2022 15:13:00

%S 1,6,455,8167302

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

%C 10^18 < a(4) < 10^19. - _Daniel Suteu_, Nov 17 2020

%H 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 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DistinctPrimeFactors.html">Distinct Prime Factors</a>.

%e a(2) = 455 because the average number of distinct prime divisors of {1..455} is >= 2.

%Y Cf. A001221, A013939, A085829, A328331, A338891.

%K nonn,more

%O 0,2

%A _Ilya Gutkovskiy_, Nov 17 2020