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A258023 Numbers of form (2^i)*(3^j) or (3^i)*(5^j).

%I A258023 #14 Sep 23 2020 03:03:54
%S A258023 1,2,3,4,5,6,8,9,12,15,16,18,24,25,27,32,36,45,48,54,64,72,75,81,96,
%T A258023 108,125,128,135,144,162,192,216,225,243,256,288,324,375,384,405,432,
%U A258023 486,512,576,625,648,675,729,768,864,972,1024,1125,1152,1215,1296
%N A258023 Numbers of form (2^i)*(3^j) or (3^i)*(5^j).
%C A258023 Union of A003586 and A003593;
%C A258023 A006530(a(n)) <= 5; A001221(a(n)) <= 2; a(n) mod 10 != 0.
%H A258023 Reinhard Zumkeller, <a href="/A258023/b258023.txt">Table of n, a(n) for n = 1..10000</a>
%H A258023 Vaclav Kotesovec, <a href="/A258023/a258023.jpg">Graph - the asymptotic ratio (65000000 terms)</a>
%F A258023 a(n) ~ exp(sqrt(2*log(2)*log(3)*log(5)*n / log(10))) / sqrt(3). - _Vaclav Kotesovec_, Sep 22 2020
%F A258023 Sum_{n>=1} 1/a(n) = 27/8. - _Amiram Eldar_, Sep 23 2020
%e A258023 .   n |  a(n) |                 n |  a(n) |
%e A258023 . ----+-------+----------     ----+-------+------------
%e A258023 .   1 |    1  |  1             16 |   32  |  2^5
%e A258023 .   2 |    2  |  2             17 |   36  |  2^2 * 3^2
%e A258023 .   3 |    3  |  3             18 |   45  |  3^2 * 5
%e A258023 .   4 |    4  |  2^2           19 |   48  |  2^4 * 3
%e A258023 .   5 |    5  |  5             20 |   54  |  2 * 3^3
%e A258023 .   6 |    6  |  2 * 3         21 |   64  |  2^6
%e A258023 .   7 |    8  |  2^3           22 |   72  |  2^3 * 3^2
%e A258023 .   8 |    9  |  3^2           23 |   75  |  3 * 5^2
%e A258023 .   9 |   12  |  2^2 * 3       24 |   81  |  3^4
%e A258023 .  10 |   15  |  3 * 5         25 |   96  |  2^5 * 3
%e A258023 .  11 |   16  |  2^4           26 |  108  |  2^2 * 3^3
%e A258023 .  12 |   18  |  2 * 3^2       27 |  125  |  5^3
%e A258023 .  13 |   24  |  2^3 * 3       28 |  128  |  2^7
%e A258023 .  14 |   25  |  5^2           29 |  135  |  3^3 * 5
%e A258023 .  15 |   27  |  3^3           30 |  144  |  2^4 * 3^2
%t A258023 n = 10^4; Join[Table[2^i*3^j, {i, 0, Log[2, n]}, {j, 0, Log[3, n/2^i]}], Table[3^i*5^j, {i, 0, Log[3, n]}, {j, 0, Log[5, n/3^i]}]] // Flatten // Union (* _Amiram Eldar_, Sep 23 2020 *)
%o A258023 (Haskell)
%o A258023 import Data.List.Ordered (union)
%o A258023 a258023 n = a258023_list !! (n-1)
%o A258023 a258023_list = union a003586_list a003593_list
%Y A258023 Cf. A003586, A003593, A051037, A006530, A001221, A010879, subsequence of: A051037, A257997, A337800, A337801.
%K A258023 nonn,easy
%O A258023 1,2
%A A258023 _Reinhard Zumkeller_, May 16 2015