Editing Harshad number (section)

{{short description|Integer divisible by sum of its digits}}
{{refimprove|date=July 2019}}
In [[mathematics]], a '''harshad number''' (or '''Niven number''') in a given [[radix|number base]] is an [[integer]] that is divisible by the [[digit sum|sum of its digits]] when written in that base.<ref>{{cite OEIS|A005349|name=Niven (or Harshad, or harshad) numbers: numbers that are divisible by the sum of their digits.|mode=cs2}} (includes only base 10 Harshad numbers).</ref> Harshad numbers in base {{mvar|n}} are also known as '''{{mvar|n}}-harshad''' (or '''{{mvar|n}}-Niven''') numbers. Because being a Harshad number is determined based on the base the number is expressed in, a number can be a Harshad number many times over.<ref>{{Cite OEIS|A080221|name=n is Harshad (divisible by the sum of its digits) in a(n) bases from 1 to n.}}</ref> So-called '''Trans-Harshad numbers''' are Harshad numbers in every base.<ref>{{Cite OEIS|A080459|name=Trans-Harshad numerals: base-10 numerals that represent positive Harshad numbers in every base in which they occur. }}</ref>

Harshad numbers were defined by [[D. R. Kaprekar]], a mathematician from [[India]].<ref>D. R. Kaprekar, ''Multidigital Numbers'', [[Scripta Mathematica]] '''21''' (1955), 27.</ref> The word "harshad" comes from the [[Sanskrit]] ''{{IAST|harṣa}}'' (joy) + ''{{IAST|da}}'' (give), meaning joy-giver. The term "Niven number" arose from a paper delivered by [[Ivan M. Niven]] at a conference on [[number theory]] in 1977.