Definition:Harshad Number

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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:

$1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 18, 20, 21, 24, 27, \ldots$

This sequence is A005349 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).

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.