Common
Harshad number
Integer divisible by sum of its digits
Harshad number
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. Because being a harshad number is determined according to the base the number is expressed in, a number can be a Harshad number many times over. So-called Trans-harshad numerals are sequences of the digits 0-9 which, in every base which uses all their digits, represent a Harshad number in that base. Harshad numbers were defined by D. R. Kaprekar, a mathematician from India. The word "harshad" comes from the Sanskrit harṣa (joy) + da (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.
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