Niven 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. 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. All integers between zero and n are n-harshad numbers.

Stated mathematically, let X be a positive integer with m digits when written in base n, and let the digits be ${\displaystyle a_{i}}$ (${\displaystyle i=0,1,\cdots ,m-1}$). (It follows that ${\displaystyle a_{i}}$ must be either zero or a positive integer up to ${\displaystyle n-1}$.) X can be expressed as

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