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In recreational mathematics, a Harshad number (or Niven number) in a given number base, is an integer that is divisible by the sum of its digits when written in that base. Harshad numbers in base ''n'' are also known as ''n''-Harshad (or ''n''-Niven) numbers. Harshad numbers were defined by D. R. Kaprekar, a mathematician from India. The word "Harshad" comes from the Sanskrit ' (joy) + ' (give), meaning joy-giver. The term “Niven number” arose from a paper delivered by Ivan M. Niven at a conference on number theory in 1977. All integers between zero and ''n'' are ''n''-Harshad numbers. == Definition == Stated mathematically, let ''X'' be a positive integer with ''m'' digits when written in base ''n'', and let the digits be ''ai'' (''i'' = 0, 1, ..., ''m'' − 1). (It follows that ''ai'' must be either zero or a positive integer up to ''n'' − 1.) ''X'' can be expressed as : If there exists an integer ''A'' such that the following holds, then ''X'' is a Harshad number in base ''n'': : A number which is a Harshad number in every number base is called an all-Harshad number, or an all-Niven number. There are only four all-Harshad numbers: 1, 2, 4, and 6 (The number 12 is a Harshad number in all bases except octal). 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「Harshad number」の詳細全文を読む スポンサード リンク
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