highly composite number

Noun

highly composite number (plural highly composite numbers)

1. A positive integer that has more divisors than any smaller positive integer.
   • In the unpublished section of his notebook, Ramanujan extends the notion of highly composite number to other arithmetic functions, mainly to Q#95;#123;2k#125;(N),#92;1#92;lek#92;le 4, where Q#95;#123;2k#125;(N) denotes the number of representations of N as the sum of 2k squares, and to...2012, George E. Andrews, Bruce C. Berndt, Ramanujan's Lost Notebook, Part III, Springer, page 359
   • Hardy has stated that a highly composite number is as unlike a prime as a number can be.1998, K. Srinivasa Rao, Srinivasa Ramanujan: A Mathematical Genius, East West Books, page 48

   Synonyms:

   HCN, antiprime

2. Used other than figuratively or idiomatically: see highly, composite number; A positive integer that has a relatively large number of divisors.
   • This factorization becomes particularly simple and economical when N is a highly composite number, in particular a power of 2.1995, Bengt Fornberg, A Practical Guide to Pseudospectral Methods, Paperback edition, Cambridge University Press, published 1998, page 176
   • However, the FFT algorithm requires that the number of input points be a highly composite number of 2ᴺ; see Rabiner and Gold (1975).2004, Roger G. Jackson, Novel Sensors and Sensing, Institute of Physics Publishing, page 275