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%I #10 Mar 01 2018 15:52:50
%S 2,3,4,9,32,256,2187,531441,134217728,70368744177664,
%T 36893488147419103232,19383245667680019896796723,
%U 713623846352979940529142984724747568191373312,13803492693581127574869511724554050904902217944340773110325048447598592
%N Greater of two consecutive 3-smooth numbers having no common divisors.
%C a(n) = A003586(A186771(n) + 1); A186927(n) = A003586(A186771(n));
%C also a subsequence of A006899: all terms are either powers of 2 or of 3.
%H Charles R Greathouse IV, <a href="/A186928/b186928.txt">Table of n, a(n) for n = 1..20</a>
%t smoothNumbers[p_, max_] := Module[{a, aa, k, pp, iter}, k = PrimePi[p]; aa = Array[a, k]; pp = Prime[Range[k]]; iter = Table[{a[j], 0, PowerExpand @ Log[pp[[j]], max/Times @@ (Take[pp, j - 1]^Take[aa, j - 1])]}, {j, 1, k}]; Table[Times @@ (pp^aa), Sequence @@ iter // Evaluate] // Flatten // Sort]; sn = smoothNumbers[3, 10^100]; Reap[For[i = 1, i <= Length[sn] - 1, i++, If[CoprimeQ[sn[[i]], sn[[i + 1]]], Sow[sn[[i + 1]]]]]][[2, 1]] (* _Jean-François Alcover_, Nov 11 2016 *)
%Y Subsequence of A006899.
%Y Cf. A186711.
%K nonn
%O 1,1
%A _Charles R Greathouse IV_ and _Reinhard Zumkeller_, Mar 01 2011
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