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A086415 Maximal exponent in prime factorization of 3-smooth numbers.

%I A086415 #14 Mar 03 2019 12:33:39
%S A086415 0,1,1,2,1,3,2,2,4,2,3,3,5,2,4,3,6,3,4,5,3,7,4,4,6,3,5,8,5,4,7,4,5,9,
%T A086415 6,4,6,8,5,5,10,7,4,6,9,6,5,11,7,8,5,6,10,7,5,12,7,9,6,6,11,8,8,5,13,
%U A086415 7,10,7,6,12,8,9,6,14,7,11,9,8,6,13,8,10,7,15,7,12,9,9,6,14,8,11,10
%N A086415 Maximal exponent in prime factorization of 3-smooth numbers.
%C A086415 a(n) = A051903(A003586(n));
%C A086415 A086414(n) <= a(n) <= A069352(n).
%H A086415 Robert Israel, <a href="/A086415/b086415.txt">Table of n, a(n) for n = 1..10000</a>
%p A086415 N:= 10^20: # to include all 3-smooth numbers <= N
%p A086415 S:= [seq(seq([2^i*3^j,max(i,j)], j=0..floor(log[3](N/2^i))),i=0..floor(log[2](N)))]:
%p A086415 map(p -> p[2], sort(S,(a,b) -> a[1]<b[1])); # _Robert Israel_, Aug 10 2014
%t A086415 M = 10^5; (* M = 10^5 gives 101 terms *)
%t A086415 S = Flatten[Table[Table[{2^i*3^j, Max[i, j]}, {j, 0, Floor[Log[3, M/2^i]]}], {i, 0, Floor[Log[2, M]]}], 1] // Sort;
%t A086415 S[[All, 2]] (* _Jean-François Alcover_, Mar 03 2019, after _Robert Israel_ *)
%Y A086415 Cf. A003586, A051903.
%Y A086415 Cf. A086414, A069352.
%K A086415 nonn
%O A086415 1,4
%A A086415 _Reinhard Zumkeller_, Jul 18 2003