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 (17671845)
“As soon as you are in a social setting, you better take away the key to the lock of your heart and pocket it; those who leave the key in the lock are fools.”
—Johann Wolfgang Von Goethe (17491832)
“It so happened that, a few weeks later, Old Ernie [Ernest Hemingway] himself was using my room in New York as a hide-out from literary columnists and reporters during one of his rare stopover visits between Africa and Key West. On such all-too-rare occasions he lends an air of virility to my dainty apartment which I miss sorely after he has gone and all the furniture has been repaired.”
—Robert Benchley (18891945)
“Players, Sir! I look on them as no better than creatures set upon tables and joint stools to make faces and produce laughter, like dancing dogs.”
—Samuel Johnson (17091784)