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Search: id:A049445
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| A049445 |
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Numbers n with property that the number of 1's in binary expansion of n (see A000120) divides n. |
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+0
10
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| 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; listen)
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OFFSET
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1,2
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COMMENT
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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
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
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FORMULA
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{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
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EXAMPLE
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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.
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MAPLE
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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
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PROGRAM
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(PARI) for(n=1, 1000, b=binary(n):l=length(b); if(n%sum(i=1, l, component(b, i))==0, print1(n, ", ")))
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CROSSREFS
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Cf. A000120, A005349.
Sequence in context: A113903 A130261 A011860 this_sequence A002174 A002202 A049225
Adjacent sequences: A049442 A049443 A049444 this_sequence A049446 A049447 A049448
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KEYWORD
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nonn,easy,nice
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AUTHOR
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njas
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EXTENSIONS
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More terms from Michael Somos
Edited by njas, Oct 07 2005 and May 16 2008
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