Harsad

Harshad numbers, also known as Niven numbers, are a specific type of number in mathematics. A number is considered a Harshad number if it is divisible by the sum of its digits. For example, the number 18 is a Harshad number because the sum of its digits (1 + 8 = 9) and 18 is divisible by 9.

The concept of Harshad numbers was introduced by Indian mathematician D.R. Kaprekar. The term "Harshad" is derived from the Sanskrit word "Hara," which means "to divide," and "Shad," which means "digit." This reflects the number's unique property of being divisible by the sum of its digits.

Harshad numbers have several interesting properties and applications in mathematics. They are often used in recreational mathematics and number theory. For instance, every prime number greater than 10 is a Harshad number. Additionally, Harshad numbers can be used to generate sequences and patterns, providing a rich area for exploration in mathematical research.

In conclusion, Harshad numbers are a fascinating subset of numbers that exhibit a unique divisibility property. Their study offers insights into number theory and has applications in various mathematical disciplines.