Search: id:A049445
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%I A049445
%S A049445 1,2,4,6,8,10,12,16,18,20,21,24,32,34,36,40,42,48,55,60,64,66,68,69,
%T A049445 72,80,81,84,92,96,108,110,115,116,120,126,128,130,132,136,138,144,
%U A049445 155,156,160,162,168,172,180,184,185,192,204,205,212,216,220,222,228
%N A049445 Numbers n with property that the number of 1's in binary expansion of 
               n (see A000120) divides n.
%C A049445 If instead of base 2 we take base 10, then we have the so-called Harshad 
               or Niven numbers (i.e. positive integers divisible by the sum of 
               their digits; A005349). - Emeric Deutsch (deutsch(AT)duke.poly.edu), 
               Apr 11 2007
%H A049445 T. D. Noe, <a href="b049445.txt">Table of n, a(n) for n=1..1000</a>
%F A049445 {n: A000120(n) | n}. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 
               03 2008
%F A049445 a(n) seems to be asymptotic to c*n*log(n) where 0.7<c<0.8 - Benoit Cloitre 
               (benoit7848c(AT)orange.fr), Jan 22 2003
%e A049445 a(7) = 12 because 12 is written 1100 in base 2 et 1+1=2 divides 12
%e A049445 n=20, binary(20)= 10100, S2(20)=2, 20/2 = 10 is integer, so n=20 belongs 
               to the sequence.
%e A049445 n=21, binary(21)= 10101, S2(21)=3, 21/3 = 7 is integer, n=21 belongs 
               to the sequence.
%p A049445 a:=proc(n) local n2: n2:=convert(n,base,2): if n mod add(n2[i],i=1..nops(n2)) 
               = 0 then n else fi end: seq(a(n),n=1..300); - Emeric Deutsch (deutsch(AT)duke.poly.edu), 
               Apr 11 2007
%o A049445 (PARI) for(n=1,1000,b=binary(n):l=length(b); if(n%sum(i=1,l, component(b,
               i))==0,print1(n,",")))
%Y A049445 Cf. A000120, A005349.
%Y A049445 Sequence in context: A113903 A130261 A011860 this_sequence A002174 A002202 
               A049225
%Y A049445 Adjacent sequences: A049442 A049443 A049444 this_sequence A049446 A049447 
               A049448
%K A049445 nonn,easy,nice
%O A049445 1,2
%A A049445 N. J. A. Sloane (njas(AT)research.att.com).
%E A049445 More terms from Michael Somos
%E A049445 Edited by N. J. A. Sloane (njas(AT)research.att.com), Oct 07 2005 and 
               May 16 2008

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