Search: id:A005349
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%I A005349 M0481
%S A005349 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,
%T A005349 63,70,72,80,81,84,90,100,102,108,110,111,112,114,117,120,126,132,133,
%U A005349 135,140,144,150,152,153,156,162,171,180,190,192,195,198,200,201,204
%N A005349 Niven (or Harshad) numbers: numbers that are divisible by the sum of 
               their digits.
%C A005349 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
%C A005349 A070635(a(n)) = 0; apart from initial term A008591 is a subsequence. 
               - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Mar 10 2008
%D A005349 R. K. Guy, The second strong law of small numbers. Math. Mag. 63 (1990), 
               no. 1, 3-20.
%D A005349 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.
%D A005349 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A005349 D. Wells, The Penguin Dictionary of Curious and Interesting Numbers. 
               Penguin Books, NY, 1986, 171.
%H A005349 N. J. A. Sloane, <a href="b005349.txt">Table of n, a(n) for n = 1..11872</
               a> (all a(n) <= 100000)
%H A005349 Jean-Marie De Koninck and Nicolas Doyon, <a href="http://www.cs.uwaterloo.ca/
               journals/JIS/index.html">Large and Small Gaps Between Consecutive 
               Niven Numbers</a>, J. Integer Seqs., Vol. 6, 2003.
%H A005349 R. E. Kennedy, <a href="http://www.trottermath.net/numthry/nivennos.html">
               Niven Numbers for Fun and Profit</a>
%H A005349 G. Villemin's Almanac of Numbers, <a href="http://www.multimania.com/
               villemingerard/Decompos/HarshadL.htm">Harshad Numbers</a>
%H A005349 G. Villemin's Almanac Of Numbers, <a href="http://www.t-mail.com/cgi-bin/
               tsail?url=http://www.multimania.com/villemingerard/Decompos/Harshad.htm&sail=full&lp=fr-en">
               Harshad Numbers</a>
%H A005349 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               HarshadNumber.html">Harshad Numbers</a>
%H A005349 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Digit.html">Link to a section of The World of Mathematics.</a>
%H A005349 Wikipedia, <a href="http://en.wikipedia.org/wiki/Harshad_number">Harshad 
               number</a>
%e A005349 195 is a term of the sequence because it is divisible by 15 (=1+9+5).
%p A005349 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)
%t A005349 Select[Range[1000], IntegerQ[ #/(Plus @@ IntegerDigits[ # ])] &] (from 
               Alonso Delarte (alonso.delarte(AT)gmail.com), Aug 04 2004)
%Y A005349 Cf. A007953, A052018, A052019, A052020, A052021, A052022, A028834.
%Y A005349 Sequence in context: A143289 A064807 A007603 this_sequence A085135 A085133 
               A110806
%Y A005349 Adjacent sequences: A005346 A005347 A005348 this_sequence A005350 A005351 
               A005352
%K A005349 nonn,base,nice,easy
%O A005349 1,2
%A A005349 N. J. A. Sloane (njas(AT)research.att.com), Robert G. Wilson v (rgwv(AT)rgwv.com)

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