Definition:Harshad Number
Jump to navigation
Jump to search
Definition
A harshad number is a positive integer which is divisible by the sum of its digits base $10$.
Hence a harshad number is a Niven number base $10$.
Sequence of Harshad Numbers
The sequence of harshad numbers begins:
- $1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 18, 20, 21, 24, 27, \ldots$
Also see
- Results about harshad numbers can be found here.
Historical Note
Harshad numbers were first described by Dattathreya Ramchandra Kaprekar.
Linguistic Note
The term harshad number comes from the Sanskrit word हर्ष (harṣa + da), which means giving joy.
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $1729$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $1729$
- Weisstein, Eric W. "Harshad Number." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/HarshadNumber.html