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In number theory, a Descartes number is an odd number which would have been an odd perfect number, if one of its composite factors were prime. They are named after René Descartes who observed that the number would be an odd perfect number if only were a prime number, since the sum-of-divisors function for would satisfy, if 22021 were prime, : where we turn a blind eye to the fact that reveals that 22021 is composite! A Descartes number is defined as an odd number where and are coprime and , whence is taken as a 'spoof' prime. The example given is the only one currently known. If is an odd almost perfect number,〔Currently, the only known almost perfect numbers are the nonnegative powers of 2, whence the only known odd almost perfect number is 〕 that is, and is taken as a 'spoof' prime, then is a Descartes number, since . If were prime, would be an odd perfect number! ==Notes== 〔 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「Descartes number」の詳細全文を読む スポンサード リンク
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