A085256 3-smooth numbers whose arithmetic derivatives are also 3-smooth.

2, 3, 4, 8, 9, 12, 16, 27, 54, 64, 81, 108, 144, 256, 432, 512, 729, 972, 1728, 2916, 3072, 3456, 4096, 6561, 11664, 19683, 20736, 23328, 27648, 65536, 78732, 139968, 157464, 186624, 262144, 442368, 531441, 944784, 1062882, 1259712, 1769472

Offset: 1

Author

Reinhard Zumkeller, Aug 11 2003

Keywords

• nonn

Comments

2^i * 3^j is a term iff 3*i + 2*j is 3-smooth, see A067371.

Examples

			144 = 2^4 * 3^2: A003415(144) = 384 = 2^7 * 3, therefore 144 is a term.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A003415, A003586, A067371.

Programs

Mathematica

s = {}; m = 14; Do[n = 3^k; While[n <= 3^m, AppendTo[s, n]; n*=2], {k, 0, m}]; ad[1] = 0; ad[n_] := n * Total @ (Last[#]/First[#] & /@ FactorInteger[n]); Select[Union[s],EulerPhi[6*(ad1 = ad[#])] == 2*ad1 && ad1 > 0 &]  (* Amiram Eldar, Jan 29 2020 *)