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.
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“There was an artist in the city of Kouroo who was disposed to strive after perfection. One day it came into his mind to make a staff. Having considered that in an imperfect work time is an ingredient, but into a perfect work time does not enter, he said to himself, It shall be perfect in all respects, though I should do nothing else in my life.”
—Henry David Thoreau (1817–1862)
“There are crimes which become innocent and even glorious through their splendor, number and excess.”
—François, Duc De La Rochefoucauld (1613–1680)