A086414 Minimal exponent in prime factorization of 3-smooth numbers.

0, 1, 1, 2, 1, 3, 2, 1, 4, 1, 1, 3, 5, 2, 1, 1, 6, 2, 4, 1, 2, 7, 2, 1, 1, 3, 5, 8, 2, 2, 1, 3, 1, 9, 2, 3, 6, 1, 3, 2, 10, 2, 4, 1, 1, 3, 3, 11, 7, 2, 4, 2, 1, 3, 4, 12, 1, 2, 4, 3, 1, 8, 3, 5, 13, 2, 2, 4, 4, 1, 1, 3, 5, 14, 3, 2, 9, 4, 5, 1, 2, 3, 5, 15, 4, 2, 1, 4, 6, 1, 3, 3, 10, 5, 16, 5, 2, 2

Offset: 1

Author

Reinhard Zumkeller, Jul 18 2003

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A003586, A051904, A069352, A086415.

Programs

Mathematica

s = {}; m = 12; Do[n = 3^k; While[n <= 3^m, AppendTo[s, n]; n*=2], {k, 0, m}]; maxExp[1] = 0; maxExp[n_] := Min @@ Last /@ FactorInteger[n]; maxExp /@ Union[s] (* Amiram Eldar, Jan 29 2020 *)

Formula

a(n) = A051904(A003586(n));

a(n) <= A086415(n) <= A069352(n).