Definition:Harshad Number
From ProofWiki
Definition
A Harshad number is a positive integer which is divisible by the sum of its digits base $10$.
Hence a Harshad number can be defined as being a Niven number base $10$.
The name comes from the Sanskrit word हर्ष (harṣa + da), which means giving joy.
It was described by D.R. Kaprekar.
Clearly all numbers of one digit are Harshad.
The first few Harshad numbers are:
- $1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 18, 20, 21, 24, 27, \ldots$
This sequence is A005349 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).
