A181309 Highly composite numbers that are not highly abundant numbers.

1084045767585249647898720000, 63958700287529729226024480000, 6086309919361329033148489516800, 30431549596806645165742447584000, 241271469053348685089061371928480000

Offset: 1

Author

T. D. Noe, Oct 13 2010

Keywords

• nonn

Comments

Numbers in A002182 but not in A002093. These terms are A002182(n) for n=255, 278, 301, 312, 362.

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?

Examples

			n1 = 1084045767585249647898720000 is not highly abundant because the smaller number
n0 = 1082074775280549193993449600 has a larger sum of divisors:
sigma(n1) = 7737797730196290039762124800
sigma(n0) = 7744678597340808238596096000
		

Links

• T. D. Noe, Table of n, a(n) for n=1..10
• L. Alaoglu and P. Erdos, On highly composite and similar numbers, Trans. Amer. Math. Soc., 56 (1944), 448-469.