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

1,4

Comments

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

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

Links

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

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]<b[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 *)

Crossrefs

Cf. A003586, A051903.

Cf. A086414, A069352.

Sequence in context: A363718 A200649 A298742 * A069013 A029281 A126792

Adjacent sequences: A086412 A086413 A086414 * A086416 A086417 A086418

Keyword

nonn

Author

Reinhard Zumkeller, Jul 18 2003

Status

approved