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%I #8 Mar 30 2012 17:27:19
%S 1084045767585249647898720000,63958700287529729226024480000,
%T 6086309919361329033148489516800,30431549596806645165742447584000,
%U 241271469053348685089061371928480000
%N Highly composite numbers that are not highly abundant numbers.
%C Numbers in A002182 but not in A002093. These terms are A002182(n) for n=255, 278, 301, 312, 362.
%C From _Matthew Vandermast_: Alaoglu and Erdos state on page 463 (just before Theorem 18) that "only a finite number of highly abundant numbers can be highly composite." What is the largest number in the intersection of the two sequences?
%H T. D. Noe, <a href="/A181309/b181309.txt">Table of n, a(n) for n=1..10</a>
%H L. Alaoglu and P. Erdos, <a href="http://www.renyi.hu/~p_erdos/1944-03.pdf">On highly composite and similar numbers,</a> Trans. Amer. Math. Soc., 56 (1944), 448-469.
%e n1 = 1084045767585249647898720000 is not highly abundant because the smaller number
%e n0 = 1082074775280549193993449600 has a larger sum of divisors:
%e sigma(n1) = 7737797730196290039762124800
%e sigma(n0) = 7744678597340808238596096000
%K nonn
%O 1,1
%A _T. D. Noe_, Oct 13 2010
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