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Numbers of form 2^i*6^j, with i, j >= 0; equivalently, numbers of the form 2^i*3^j with 0 <= j <= i.
12

%I #17 Sep 19 2022 09:57:30

%S 1,2,4,6,8,12,16,24,32,36,48,64,72,96,128,144,192,216,256,288,384,432,

%T 512,576,768,864,1024,1152,1296,1536,1728,2048,2304,2592,3072,3456,

%U 4096,4608,5184,6144,6912,7776,8192,9216,10368,12288,13824,15552,16384,18432

%N Numbers of form 2^i*6^j, with i, j >= 0; equivalently, numbers of the form 2^i*3^j with 0 <= j <= i.

%H Charles R Greathouse IV, <a href="/A025610/b025610.txt">Table of n, a(n) for n = 1..10000</a>

%F From _Vaclav Kotesovec_, Sep 25 2020: (Start)

%F a(n) ~ exp(sqrt(2*log(2)*log(6)*n)) / sqrt(12).

%F Sum_{k>=1} 1/a(k) = 12/5. (End)

%t n = 10^6; Flatten[Table[2^i*6^j, {i, 0, Log2[n]}, {j, 0, Log[6, n/2^i]}]] // Sort (* _Amiram Eldar_, Sep 26 2020 *)

%o (PARI) list(lim)=my(v=List(),t); for(j=0,logint(lim\=1,6), t=6^j; while(t<=lim, listput(v,t); t<<=1)); Set(v) \\ _Charles R Greathouse IV_, Dec 14 2016

%Y Intersection of A025487 and A003586.

%K easy,nonn

%O 1,2

%A _David W. Wilson_