|
| |
|
|
A049445
|
|
Numbers n with property that the number of 1's in binary expansion of n (see A000120) divides n.
|
|
16
| |
|
|
1, 2, 4, 6, 8, 10, 12, 16, 18, 20, 21, 24, 32, 34, 36, 40, 42, 48, 55, 60, 64, 66, 68, 69, 72, 80, 81, 84, 92, 96, 108, 110, 115, 116, 120, 126, 128, 130, 132, 136, 138, 144, 155, 156, 160, 162, 168, 172, 180, 184, 185, 192, 204, 205, 212, 216, 220, 222, 228
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,2
|
|
|
COMMENTS
| 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
A199238(a(n)) = 0. [Reinhard Zumkeller, Nov 04 2011]
|
|
|
LINKS
| T. D. Noe, Table of n, a(n) for n=1..1000
|
|
|
FORMULA
| {n: A000120(n) | n}. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 03 2008
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
|
|
|
EXAMPLE
| a(7) = 12 because 12 is written 1100 in base 2 et 1+1=2 divides 12
n=20, binary(20)= 10100, S2(20)=2, 20/2 = 10 is integer, so n=20 belongs to the sequence.
n=21, binary(21)= 10101, S2(21)=3, 21/3 = 7 is integer, n=21 belongs to the sequence.
|
|
|
MAPLE
| 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
|
|
|
MATHEMATICA
| ok[n_] := Divisible[n, Count[ IntegerDigits[n, 2], 1] ]; Select[ Range[228], ok] (* From Jean-François Alcover, Dec 01 2011 *)
|
|
|
PROG
| (PARI) for(n=1, 1000, b=binary(n):l=length(b); if(n%sum(i=1, l, component(b, i))==0, print1(n, ", ")))
(Haskell)
a049445 n = a049445_list !! (n-1)
a049445_list = map (+ 1) $ elemIndices 0 a199238_list
-- Reinhard Zumkeller, Nov 04 2011
|
|
|
CROSSREFS
| Cf. A000120, A005349.
Sequence in context: A130261 A186384 A011860 * A002174 A002202 A049225
Adjacent sequences: A049442 A049443 A049444 * A049446 A049447 A049448
|
|
|
KEYWORD
| nonn,easy,nice,base
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
|
|
EXTENSIONS
| More terms from Michael Somos
Edited by N. J. A. Sloane (njas(AT)research.att.com), Oct 07 2005 and May 16 2008
|
| |
|
|
