|
In number theory, a semiperfect number or pseudoperfect number is a natural number ''n'' that is equal to the sum of all or some of its proper divisors. A semiperfect number that is equal to the sum of all its proper divisors is a perfect number. The first few semiperfect numbers are :6, 12, 18, 20, 24, 28, 30, 36, 40, ... == Properties == * Every multiple of a semiperfect number is semiperfect.〔Zachariou+Zachariou (1972)〕 A semiperfect number that is not divisible by any smaller semiperfect number is ''primitive''. * Every number of the form 2''m''''p'' for a natural number ''m'' and a prime number ''p'' such that ''p'' < 2''m'' + 1 is also semiperfect. * * In particular, every number of the form 2''m'' − 1(2''m'' − 1) is semiperfect, and indeed perfect if 2''m'' − 1 is a Mersenne prime. * The smallest odd semiperfect number is 945 (see, e.g., Friedman 1993). * A semiperfect number is necessarily either perfect or abundant. An abundant number that is not semiperfect is called a weird number. * With the exception of 2, all primary pseudoperfect numbers are semiperfect. * Every practical number that is not a power of two is semiperfect. * The natural density of the set of semiperfect numbers exists.〔Guy (2004) p. 75〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Semiperfect number」の詳細全文を読む スポンサード リンク
|