A186928 Greater of two consecutive 3-smooth numbers having no common divisors.

2, 3, 4, 9, 32, 256, 2187, 531441, 134217728, 70368744177664, 36893488147419103232, 19383245667680019896796723, 713623846352979940529142984724747568191373312, 13803492693581127574869511724554050904902217944340773110325048447598592

Offset: 1

Author

Charles R Greathouse IV and Reinhard Zumkeller, Mar 01 2011

Keywords

• nonn

Comments

a(n) = A003586(A186771(n) + 1); A186927(n) = A003586(A186771(n));

also a subsequence of A006899: all terms are either powers of 2 or of 3.

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..20

Crossrefs

Subsequence of A006899.

Cf. A186711.

Programs

Mathematica

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 *)