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 A085256 3-smooth numbers whose arithmetic derivatives are also 3-smooth. 1
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 2^i * 3^j is a term iff 3*i + 2*j is 3-smooth, see A067371. LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 EXAMPLE 144 = 2^4 * 3^2: A003415(144) = 384 = 2^7 * 3, therefore 144 is a term. 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 *) CROSSREFS Cf. A003415, A003586, A067371. Sequence in context: A023786 A018231 A332622 * A335761 A127483 A130804 Adjacent sequences:  A085253 A085254 A085255 * A085257 A085258 A085259 KEYWORD nonn AUTHOR Reinhard Zumkeller, Aug 11 2003 STATUS approved

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Last modified August 15 23:32 EDT 2022. Contains 356150 sequences. (Running on oeis4.)