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%I #33 May 06 2021 08:11:44
%S 3,37,42719,5737850066077
%N Least prime p such that more than half of all integers are divisible by n distinct primes not greater than p.
%C The proportion of all integers that satisfy the divisibility criterion for p=prime(m) is determined using the proportion that satisfy it over any interval of primorial(m)=A002110(m) integers.
%C a(4) is from De Koninck, 2009; calculation credited to D Grégoire.
%D J.-M. De Koninck, Those Fascinating Numbers, American Mathematical Society, 2009.
%H J. de Koninck and G. Tenenbaum, <a href="https://doi.org/10.1017/S0305004102005972">Sur la loi de répartition du k-ième facteur premier d'un entier</a>, Mathematical Proceedings of the Cambridge Philosophical Society, 133(2), 191-204. doi:10.1017/S0305004102005972
%H Gérald Tenenbaum, <a href="https://hal.archives-ouvertes.fr/hal-01281530/document">Some of Erdos' unconventional problems in number theory, thirty-four years later.</a> Erdos Centennial, Janos Bolyai Math. Soc., 2013, 651-681. HAL Id: hal-01281530
%F a(n) is least p=prime(m) such that 2*Sum_{k=0..n-1} A096294(m,k) < A002110(m).
%e Exactly half of the integers are divisible by 2, so a(1)>2. Two-thirds of all integers are divisible by 2 or 3, so a(1) = 3.
%Y Cf. A002110, A096294, A194156, A281889.
%K nonn,more,hard
%O 1,1
%A _Peter Munn_, Mar 26 2017
%E Definition edited by _N. J. A. Sloane_, Apr 01 2017
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