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almost perfect number
In mathematics, an almost perfect number (sometimes also called slightly defective or least deficient number) is a natural number ''n'' such that the sum of all divisors of ''n'' (the sum-of-divisors function ''σ''(''n'')) is equal to 2''n'' − 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 . Therefore the only known odd almost perfect number is 20 = 1, and the only known even almost perfect numbers are those of the form 2''k'' for some positive number ''k''; however, it has not been shown that all almost perfect numbers are of this form. It is known that an odd almost perfect number greater than 1 would have at least 6 prime factors.
If ''m'' is an odd almost perfect number then is a Descartes number. Moreover if ''a'' and ''b'' are positive odd integers such that
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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