Back عدد هرشد Arabic Лікі харшад BE-X-OLD Harshad-tal Danish Harshad-Zahl German Número de Harshad Spanish Harshad-luku Finnish Nombre harshad French מספר הרשאד HE Harshad-számok Hungarian Հարշադի թվեր Armenian
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In mathematics, a harshad number (or Niven number) in a given number base is an integer that is divisible by the sum of its digits when written in that base.[1] Harshad numbers in base n are also known as n-harshad (or 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.[2] So-called Trans-Harshad numbers are Harshad numbers in every base.[3]
Harshad numbers were defined by D. R. Kaprekar, a mathematician from India.[4] The word "harshad" comes from the Sanskrit harṣa (joy) + 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.
- ^ Sloane, N. J. A. (ed.), "Sequence A005349 (Niven (or Harshad, or harshad) numbers: numbers that are divisible by the sum of their digits.)", The On-Line Encyclopedia of Integer Sequences, OEIS Foundation (includes only base 10 Harshad numbers).
- ^ Sloane, N. J. A. (ed.). "Sequence A080221 (n is Harshad (divisible by the sum of its digits) in a(n) bases from 1 to n.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A080459 (Trans-Harshad numerals: base-10 numerals that represent positive Harshad numbers in every base in which they occur.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ D. R. Kaprekar, Multidigital Numbers, Scripta Mathematica 21 (1955), 27.