A264164 3-smooth numbers whose number of divisors is not 3-smooth.
16, 48, 64, 81, 144, 162, 192, 324, 432, 512, 576, 648, 729, 1024, 1296, 1458, 1536, 1728, 2592, 2916, 3072, 3888, 4096, 4608, 5184, 5832, 8192, 9216, 10368, 11664, 12288, 13824, 15552, 16384, 19683, 20736, 23328, 24576, 27648, 34992, 36864, 39366, 41472
Offset: 1
Keywords
Examples
a(12) = 648 = 2^3*3^4 = A003586(36) and A000005(648) = 20 = 2^2*5. a(13) = 729 = 3^6 = A003586(37) and A000005(729) = 7. A003586(38) = 768 = 2^8*3 is not a term, as A000005(768) = 18 = 2*3^2.
Links
- Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Programs
-
Haskell
a264164 n = a264164_list !! (n-1) a264164_list = filter ((== 0) . a065333 . a000005') a003586_list
-
Mathematica
smQ[n_] := n == Times @@ ({2, 3}^IntegerExponent[n, {2, 3}]); seq[max_] := Sort@ Flatten@ Table[If[smQ[i + 1] && smQ[j + 1], Nothing, 2^i * 3^j], {i, 0 , Log2[max]}, {j, 0, Log[3, max/2^i]}]; seq[42000] (* Amiram Eldar, Sep 03 2023 *)