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%I #9 Oct 19 2016 15:08:36
%S 0,2,4,16,16,64,128,384,256,1024,2048,6144,8192,24576,49152,131072,
%T 65536,262144,524288,1572864,2097152,6291456,12582912,33554432,
%U 33554432,100663296,201326592,536870912,805306368,2147483648,4294967296
%N a(n) = S2(n)*2^n; where S2(n) is digit sum of n, n in binary notation.
%H G. C. Greubel, <a href="/A135569/b135569.txt">Table of n, a(n) for n = 0..1000</a>
%F For all n we have 2/n <= a(n+1)/a(n)<= 4. This holds because a(2^n -1)= n*2^(2^n -1); a(2^n) = 2^2^n; a(2^n +1) = 4*2^2^n.
%F a(n) = A000120(n)*2^n. - _R. J. Mathar_, Mar 03 2008
%p A000120 := proc(n) add(i,i=convert(n,base,2)) ; end: A135569 := proc(n) A000120(n)*2^n ; end: seq(A135569(n),n=0..80) ; # _R. J. Mathar_, Mar 03 2008
%t Table[DigitCount[n, 2, 1]*2^n, {n, 0, 25}] (* _G. C. Greubel_, Oct 19 2016 *)
%Y Cf. A000120, A010060.
%K easy,nonn,base
%O 0,2
%A _Ctibor O. Zizka_, Feb 23 2008, Mar 03 2008
%E Corrected and extended by _R. J. Mathar_, Mar 03 2008
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