An 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 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 Niven numbers take their name from Ivan M. Niven from a paper delivered at a conference on number theory in 1997. All integers between zero and n are Harshad numbers in base n.
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:
It is further noted that all the numbers on this website are sequentially generated, so any correspondence between them and your phone number is to be considered purely accidental.
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