A264165 - OEIS

%I #14 Sep 03 2023 08:43:44

%S 1,2,3,4,6,8,9,12,18,24,27,32,36,54,72,96,108,128,216,243,256,288,384,

%T 486,768,864,972,1152,1944,2048,2187,2304,3456,4374,6144,6561,6912,

%U 7776,8748,13122,17496,18432,26244,31104,32768,52488,55296,62208,69984

%N 3-smooth numbers whose number of divisors is 3-smooth.

%H Reinhard Zumkeller, <a href="/A264165/b264165.txt">Table of n, a(n) for n = 1..2000</a>

%F A065333(a(n)) * A065333(A000005(a(n))) = 1.

%e a(25) = 768 = 2^8*3 = A003586(38) and A000005(768) = 18 = 2*3^2;

%e a(26) = 864 = 2^5*3^3 = A003586(39) and A000005(864) = 24 = 2^3*3;

%e a(27) = 972 = 2^2*3^5 = A003586(40) and A000005(972) = 18 = 2*3^2;

%e but A003586(41) = 1024 = 2^10 is not a term, as A000005(1024) = 11.

%t smQ[n_] := n == Times @@ ({2, 3}^IntegerExponent[n, {2, 3}]);

%t seq[max_] := Sort@ Flatten@ Table[2^i * 3^j, {i, Select[Range[0, Floor[Log2[max]]], smQ[# + 1] &]}, {j, Select[Range[0, Floor[Log[3, max/2^i]]], smQ[# + 1] &]}]; seq[70000] (* _Amiram Eldar_, Sep 03 2023 *)

%o (Haskell)

%o a264165 n = a264165_list !! (n-1)

%o a264165_list = filter ((== 1) . a065333 . a000005') a003586_list

%Y Cf. A000005, A003586, A065333, A264164 (complement with respect to A003586).

%K nonn

%O 1,2

%A _Reinhard Zumkeller_, Nov 19 2015