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%I #10 Jul 13 2019 03:58:07
%S 2557,6736,9043,9809,13493,15948,16839,20848,23926,29662,30930,31251,
%T 31826,33020,35600,36596,54953,56525,59945,59953,64925,66631,69122,
%U 69290,70333,70546,77968,78024,83027,84000,84025,91790,91918,100458,100850,101100,107151
%N Numbers k such that there is no prime p and index j > k such that A002182(j) = p * A002182(k).
%C Indices k such that the k-th highly composite number cannot be obtained by dividing any larger highly composite number by a prime.
%C This is a sequence of counterexamples to the first conjecture by Alaoglu & Erdős that such highly composite numbers do not exist. Robin found the first counterexample: A002182(2557) = 3.000... * 10^153. The sequence of counterexamples to their second conjecture is A272606.
%H Amiram Eldar, <a href="/A309042/b309042.txt">Table of n, a(n) for n = 1..122</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, A272606.
%K nonn
%O 1,1
%A _Amiram Eldar_, Jul 09 2019
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