A264165 3-smooth numbers whose number of divisors is 3-smooth.

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 32, 36, 54, 72, 96, 108, 128, 216, 243, 256, 288, 384, 486, 768, 864, 972, 1152, 1944, 2048, 2187, 2304, 3456, 4374, 6144, 6561, 6912, 7776, 8748, 13122, 17496, 18432, 26244, 31104, 32768, 52488, 55296, 62208, 69984

Offset: 1

Author

Reinhard Zumkeller, Nov 19 2015

Keywords

• nonn

Examples

			a(25) = 768 = 2^8*3 = A003586(38) and A000005(768) = 18 = 2*3^2;
a(26) = 864 = 2^5*3^3 = A003586(39) and A000005(864) = 24 = 2^3*3;
a(27) = 972 = 2^2*3^5 = A003586(40) and A000005(972) = 18 = 2*3^2;
but A003586(41) = 1024 = 2^10 is not a term, as A000005(1024) = 11.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..2000

Crossrefs

Cf. A000005, A003586, A065333, A069353, A264164 (complement with respect to A003586).

Programs

Haskell

a264165 n = a264165_list !! (n-1)
a264165_list = filter ((== 1) . a065333 . a000005') a003586_list

Mathematica

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

Formula

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

Sum_{n>=1} 1/a(n) = (Sum_{n>=1} 1/2^A069353(n)) * (Sum_{n>=1} 1/3^A069353(n)) = 2.85129093516260954847... . - Amiram Eldar, Apr 17 2025