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%I #21 Nov 13 2023 09:07:37
%S 5,10,11,15,17,20,22,23,29,30,33,34,35,40,41,44,45,46,47,51,53,58,59,
%T 60,65,66,68,69,70,71,77,80,82,83,87,88,89,90,92,94,95,99,101,102,105,
%U 106,107,113,116,118,119,120,123,125,130,131,132,135,136,137,138
%N Numbers of form 2^i*3^j*(6k+5), i, j, k >= 0.
%C Are a(n) > A225837(n) for all n? - _Zak Seidov_, May 17 2013
%C Yes. Imagine every 3-smooth number, m, visits you regularly, depositing a gold coin for safe keeping at each epoch (6k+1)*m and collecting it at epoch (6k+5)*m. If you run out of coins, you are doing something other than keeping them in a vault! - _Peter Munn_, Nov 13 2023
%C The asymptotic density of this sequence is 1/2. - _Amiram Eldar_, Apr 03 2022
%H Zak Seidov, <a href="/A225838/b225838.txt">Table of n, a(n) for n = 1..10000</a>
%H Zak Seidov, <a href="/A225838/a225838.jpg">Graph of A225838(n) - A225837(n) for n=1..126454.</a>
%t mx = 153; t = {}; Do[n = 2^i*3^j (6 k + 5); If[n <= mx, AppendTo[t, n]], {i, 0, Log[2, mx]}, {j, 0, Log[3, mx]}, {k, 0, mx/6}]; Union[t] (* _T. D. Noe_, May 16 2013 *)
%o (PARI) for(n=1,200,t=n/(2^valuation(n,2)*3^valuation(n,3));if((t%6==5),print1(n,",")))
%o (Magma) [n: n in [1..200] | d mod 6 eq 5 where d is n div (2^Valuation(n,2)*3^Valuation(n,3))]; // _Bruno Berselli_, May 16 2013
%Y Complement of A225837.
%Y Symmetric difference of A003159 and A026225; of A189716 and A325424.
%K nonn,easy
%O 1,1
%A _Ralf Stephan_, May 16 2013
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