This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A284411 #47 Mar 09 2025 05:16:50
%S A284411 3,37,42719,5737850066077
%N A284411 Least prime p such that more than half of all integers are divisible by n distinct primes not greater than p.
%C A284411 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 A284411 a(4) is from De Koninck, 2009; calculation credited to David Grégoire.
%C A284411 a(5) is about 7.887*10^34 assuming the Riemann Hypothesis, and about 7*10^34 unconditionally (De Koninck and Tenenbaum, 2002). - _Amiram Eldar_, Dec 05 2024
%D A284411 Jean-Marie De Koninck, Those Fascinating Numbers, American Mathematical Society, 2009, pp. 13, 216 and 368.
%H A284411 Jean-Marie De Koninck and Gérald 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, Vol. 133, No. 2 (2002), pp. 191-204.
%H A284411 Gérald Tenenbaum, <a href="https://hal.archives-ouvertes.fr/hal-01281530/document">Some of Erdős' unconventional problems in number theory, thirty-four years later</a>, Erdős Centennial, Janos Bolyai Math. Soc., 2013, 651-681. HAL Id: hal-01281530.
%F A284411 a(n) is least p=prime(m) such that 2*Sum_{k=0..n-1} A096294(m,k) < A002110(m).
%F A284411 log(log(a(n))) = n - b + O(1/sqrt(n)), where b = 1/3 + A077761 (De Koninck and Tenenbaum, 2002). - _Amiram Eldar_, Dec 05 2024
%e A284411 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 A284411 Cf. A002110, A077761, A096294, A194156, A281889.
%Y A284411 Cf. A038110, A038111, A342479, A342480, A378720, A378721.
%K A284411 nonn,more,hard
%O A284411 1,1
%A A284411 _Peter Munn_, Mar 26 2017
%E A284411 Definition edited by _N. J. A. Sloane_, Apr 01 2017