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

1,1

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Formula

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

Example

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;
but A003586(38) = 768 = 2^8*3 is not a term, as A000005(768) = 18 = 2*3^2.

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 *)

Prog

(Haskell)
a264164 n = a264164_list !! (n-1)
a264164_list = filter ((== 0) . a065333 . a000005') a003586_list

Crossrefs

Cf. A000005, A003586, A065333, A264165 (complement with respect to A003586).

Sequence in context: A322448 A374588 A354181 * A045047 A239344 A195087

Adjacent sequences: A264161 A264162 A264163 * A264165 A264166 A264167

Keyword

nonn

Author

Reinhard Zumkeller, Nov 19 2015

Status

approved