highly composite number
Word Rarity
Rare
Frequency: Zipf frequency 3.89 in modern English
41
Scrabble Score
21
Letters
6
Syllables
16
Unique Chars
Meaning
noun
Used other than figuratively or idiomatically: see highly, composite number; A positive integer that has a relatively large number of divisors.
Example Sentences
- "In the unpublished section of his notebook, Ramanujan extends the notion of highly composite number to other arithmetic functions, mainly to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 #92;sigma#95;#123;-s#125;(N), where #92;sigma#95;#123;-s#125;(N) denotes the sum of the (-s)th powers of the divisors of N."
- "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."
- "A highly composite number, then, was in Hardy's phrase "as unlike a prime as a number can be." Ramanujan had explored their properties for some time; in the earliest pages of his second notebook he'd listed about a hundred highly composite numbers−the first few are 2, 4, 6, 12, 24, 36, 48, 60, 120−searching for patterns. He found them."
- "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)."