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Search: id:A005349
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| A005349 |
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Niven (or Harshad) numbers: numbers that are divisible by the sum of their digits.
(Formerly M0481)
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+0
96
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| 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 18, 20, 21, 24, 27, 30, 36, 40, 42, 45, 48, 50, 54, 60, 63, 70, 72, 80, 81, 84, 90, 100, 102, 108, 110, 111, 112, 114, 117, 120, 126, 132, 133, 135, 140, 144, 150, 152, 153, 156, 162, 171, 180, 190, 192, 195, 198, 200, 201, 204
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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z-Niven numbers are numbers n which are divisible by (A*s(n)+ B) where A,B are integers and s(n) is sum of digits of n. Niven numbers have A=1, B=0. - Ctibor O. ZIZKA (ctibor.zizka(AT)seznam.cz), Feb 23 2008
A070635(a(n)) = 0; apart from initial term A008591 is a subsequence. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Mar 10 2008
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REFERENCES
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R. K. Guy, The second strong law of small numbers. Math. Mag. 63 (1990), no. 1, 3-20.
R. E. Kennedy and C. N. Cooper, On the natural density of the Niven numbers, Abstract 816-11-219, Abstracts Amer. Math. Soc., 6 (1985), 17.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
D. Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, 171.
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LINKS
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N. J. A. Sloane, Table of n, a(n) for n = 1..11872 (all a(n) <= 100000)
Jean-Marie De Koninck and Nicolas Doyon, Large and Small Gaps Between Consecutive Niven Numbers, J. Integer Seqs., Vol. 6, 2003.
R. E. Kennedy, Niven Numbers for Fun and Profit
G. Villemin's Almanac of Numbers, Nomres de Harshad
G. Villemin's Almanac of Numbers, Numbers of Harshad
Eric Weisstein's World of Mathematics, Harshad Numbers
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Wikipedia, Harshad number
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EXAMPLE
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195 is a term of the sequence because it is divisible by 15 (=1+9+5).
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MAPLE
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s:=proc(n) local N:N:=convert(n, base, 10):sum(N[j], j=1..nops(N)) end:p:=proc(n) if floor(n/s(n))=n/s(n) then n else fi end: seq(p(n), n=1..210); (Deutsch)
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MATHEMATICA
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Select[Range[1000], IntegerQ[ #/(Plus @@ IntegerDigits[ # ])] &] (from Alonso Delarte (alonso.delarte(AT)gmail.com), Aug 04 2004)
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CROSSREFS
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Cf. A007953, A052018, A052019, A052020, A052021, A052022, A028834.
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KEYWORD
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nonn,base,nice,easy,new
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Robert G. Wilson v (rgwv(AT)rgwv.com)
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EXTENSIONS
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Villemin links fixed by Robert Munafo (mrob27(AT)gmail.com), Dec 14 2009
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