OFFSET
1,2
COMMENTS
Indices k such that the k-th highly composite number cannot be obtained by multiplying any smaller highly composite number by a prime.
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
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..77 (Calculated from Achim Flammenkamp's List of the first 779,674 highly composite numbers)
Leonidas Alaoglu and Paul Erdős, On highly composite and similar numbers, Transactions of the American Mathematical Society, Vol. 56, No. 3 (1944), pp. 448-469. See p. 467.
Achim Flammenkamp, Highly Composite Numbers.
Guy Robin, Méthodes d'optimisation pour un problème de théorie des nombres, RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Vol. 17, No. 3 (1983), pp. 239-247.
CROSSREFS
KEYWORD
nonn
AUTHOR
Joerg Arndt, Nov 01 2016
EXTENSIONS
a(7)-a(37) from Amiram Eldar, Jul 09 2019
STATUS
approved