In Mathematics
Eighteen is a composite number, its proper divisors being 1, 2, 3, 6 and 9. Three of these divisors (3, 6 and 9) add up to 18, hence 18 is a semiperfect number. Eighteen is the first inverted square-prime of the form p.q2.
It is a heptagonal number, and as the sum of the first three pentagonal numbers, it is a pentagonal pyramidal number. It is also the sum of the totient function for the first seven integers. It is the sixth lucas number.
Eighteen is the second abundant number with the aliquot sum of 21 (117% in abundance) in the aliquot sequence (18, 21, 11, 1, 0) thus being the first composite number in the 11-aliquot tree. Eighteen is the aliquot sum of only one number the square 289.
In base 10 it is a Harshad number.
18, aside from 0, is the only number that equals twice the sum of its decimal digits.
Read more about this topic: 18 (number)
Famous quotes containing the word mathematics:
“In mathematics he was greater
Than Tycho Brahe, or Erra Pater:
For he, by geometric scale,
Could take the size of pots of ale;
Resolve, by sines and tangents straight,
If bread and butter wanted weight;
And wisely tell what hour o’ th’ day
The clock doth strike, by algebra.”
—Samuel Butler (1612–1680)
“The three main medieval points of view regarding universals are designated by historians as realism, conceptualism, and nominalism. Essentially these same three doctrines reappear in twentieth-century surveys of the philosophy of mathematics under the new names logicism, intuitionism, and formalism.”
—Willard Van Orman Quine (b. 1908)