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

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, 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, 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

Offset: 1

Author

Reinhard Zumkeller, Jul 18 2003

Keywords

• nonn

Comments

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

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

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A003586, A051903.

Cf. A086414, A069352.

Programs

Maple

N:= 10^20: # to include all 3-smooth numbers <= N
S:= [seq(seq([2^i*3^j,max(i,j)], j=0..floor(log[3](N/2^i))),i=0..floor(log[2](N)))]:
map(p -> p[2], sort(S,(a,b) -> a[1]Robert Israel, Aug 10 2014

Mathematica

M = 10^5; (* M = 10^5 gives 101 terms *)
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;
S[[All, 2]] (* Jean-François Alcover, Mar 03 2019, after Robert Israel *)