Key To The Tables
- d(n) is the number of positive divisors of n, including 1 and n itself
- σ(n) is the sum of all the positive divisors of n, including 1 and n itself
- s(n) is the sum of the proper divisors of n, which does not include n itself; that is, s(n) = σ(n) − n
- a perfect number equals the sum of its proper divisors; that is, s(n) = n; the only perfect numbers between 1 and 1000 are 6, 28 and 496
- amicable numbers and sociable numbers are numbers where the sum of their proper divisors form a cycle; the only examples below 1000 are 220 and 284
- a deficient number is greater than the sum of its proper divisors; that is, s(n) < n
- an abundant number is less than the sum of its proper divisors; that is, s(n) > n
- a prime number has only 1 and itself as divisors; that is, d(n) = 2. Prime numbers are always deficient as s(n)=1
Read more about this topic: Table Of Divisors
Famous quotes containing the words key to the, key to, key and/or tables:
“The safety of the republic being the supreme law, and Texas having offered us the key to the safety of our country from all foreign intrigues and diplomacy, I say accept the key ... and bolt the door at once.”
—Andrew Jackson (1767–1845)
“There are two kinds of timidity—timidity of mind, and timidity of the nerves; physical timidity, and moral timidity. Each is independent of the other. The body may be frightened and quake while the mind remains calm and bold, and vice versë. This is the key to many eccentricities of conduct. When both kinds meet in the same man he will be good for nothing all his life.”
—Honoré De Balzac (1799–1850)
“Experience has shown that the trade of the East is the key to national wealth and influence.”
—Chester A. Arthur (1829–1886)
“Eddie Felson: Church of the Good Hustler.
Charlie: Looks more like a morgue to me. Those tables are the slabs they lay the stiffs on.
Eddie Felson: I’ll be alive when I get out, Charlie.”
—Sydney Carroll, U.S. screenwriter, and Robert Rossen. Eddie Felson (Paul Newman)