A181309 Highly composite numbers that are not highly abundant numbers.

1084045767585249647898720000, 63958700287529729226024480000, 6086309919361329033148489516800, 30431549596806645165742447584000, 241271469053348685089061371928480000

Offset

1,1

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?

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.

Example

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

Crossrefs

Sequence in context: A217413 A217428 A146561 * A095448 A105298 A003853

Adjacent sequences: A181306 A181307 A181308 * A181310 A181311 A181312

Keyword

nonn

Author

T. D. Noe, Oct 13 2010

Status

approved