Almost Perfect Number

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:

    Every perfect life is a parable invented by God.
    Simone Weil (1909–1943)

    I have known a number of Don Juans who were good studs and who cavorted between the sheets without a psychiatrist to guide them. But most of the busy love-makers I knew were looking for masculinity rather than practicing it. They were fellows of dubious lust.
    Ben Hecht (1893–1964)