highly composite number

Etymology

Definitions

1. 1

   A positive integer that has more divisors than any smaller positive integer.

   • Hardy has stated that a highly composite number is as unlike a prime as a number can be.
   • Ramanujan devoted a section of his paper to the study of Q(x), the number of highly composite numbers #92;lex Since d(2n)gt;d(n), we see that between x and 2x, there is always a highly composite number.
2. 2

   Used other than figuratively or idiomatically

   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.
   • However, the FFT algorithm requires that the number of input points be a highly composite number of 2ᴺ; see Rabiner and Gold (1975).
   • We then derive the fast Fourier transform for any highly composite number n. In many applications n is a power of 2, but this choice is hardly necessary.

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