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%I #15 Jul 09 2019 15:26:25
%S 1,815,4372,4996,5312,5442,22093,24931,24964,25587,26064,28776,29365,
%T 29372,32757,34115,34122,36046,51207,52527,54746,57927,58971,63160,
%U 63988,63993,82127,95661,95746,97931,128049,132331,132720,134358,136254,150282,179341
%N Numbers k such that there is no prime p and index j < k such that A002182(k) = p * A002182(j).
%C Indices k such that the k-th highly composite number cannot be obtained by multiplying any smaller highly composite number by a prime.
%C This is a sequence of counterexamples to the second conjecture by Alaoglu & Erdős that such highly composite numbers do not exist (they did not consider 1 to be highly composite number). Robin found the first 3 counterexamples: A002182(815) = 3.622... * 10^65, A002182(4372) = 6.043... * 10^220, and A002182(4996) = 1.115 * 10^244. - _Amiram Eldar_, Jul 09 2019
%H Amiram Eldar, <a href="/A272606/b272606.txt">Table of n, a(n) for n = 1..77</a> (Calculated from Achim Flammenkamp's List of the first 779,674 highly composite numbers)
%H Leonidas Alaoglu and Paul Erdős, <a href="https://doi.org/10.1090/S0002-9947-1944-0011087-2">On highly composite and similar numbers</a>, Transactions of the American Mathematical Society, Vol. 56, No. 3 (1944), pp. 448-469. See p. 467.
%H Achim Flammenkamp, <a href="http://wwwhomes.uni-bielefeld.de/achim/highly.html">Highly Composite Numbers</a>.
%H Guy Robin, <a href="https://eudml.org/doc/92187">Méthodes d'optimisation pour un problème de théorie des nombres</a>, RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Vol. 17, No. 3 (1983), pp. 239-247.
%Y Cf. A002182.
%K nonn
%O 1,2
%A _Joerg Arndt_, Nov 01 2016
%E a(7)-a(37) from _Amiram Eldar_, Jul 09 2019
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