In mathematics, an almost perfect number (sometimes also called slightly defective number) is a natural number n such that the sum of all divisors of n (the divisor function σ(n)) is equal to 2n - 1, the sum of all proper divisors of n, s(n) = σ(n) - n, then being equal to n - 1. The only known almost perfect numbers are powers of 2 with non-negative exponents (sequence A000079 in OEIS). Therefore the only known odd almost perfect number is 20 = 1, and the only known even almost perfect numbers are those of the form 2k for some positive number k; however, it has not been shown that all almost perfect numbers are of this form. Almost perfect numbers are also known as least deficient numbers.
Famous quotes containing the words perfect and/or number:
“So much of our lives is given over to the consideration of our imperfections that there is no time to improve our imaginary virtues. The truth is we only perfect our vices, and man is a worse creature when he dies than he was when he was born.”
—Edward Dahlberg (1900–1977)
“The said truth is that it is the greatest happiness of the greatest number that is the measure of right and wrong.”
—Jeremy Bentham (1748–1832)