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A086415
Maximal exponent in prime factorization of 3-smooth numbers.
7
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
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
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Jul 18 2003
STATUS
approved