A086415 - OEIS

%I #14 Mar 03 2019 12:33:39

%S 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 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 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 Maximal exponent in prime factorization of 3-smooth numbers.

%C a(n) = A051903(A003586(n));

%C A086414(n) <= a(n) <= A069352(n).

%H Robert Israel, <a href="/A086415/b086415.txt">Table of n, a(n) for n = 1..10000</a>

%p N:= 10^20: # to include all 3-smooth numbers <= N

%p 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 map(p -> p[2], sort(S,(a,b) -> a[1]<b[1])); # _Robert Israel_, Aug 10 2014

%t M = 10^5; (* M = 10^5 gives 101 terms *)

%t 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 S[[All, 2]] (* _Jean-François Alcover_, Mar 03 2019, after _Robert Israel_ *)

%Y Cf. A003586, A051903.

%Y Cf. A086414, A069352.

%K nonn

%O 1,4

%A _Reinhard Zumkeller_, Jul 18 2003