A065335 3-exponents to represent 3-smooth numbers (A065332).

0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 1

Author

Reinhard Zumkeller, Oct 29 2001

Keywords

• nonn

Links

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

Crossrefs

Cf. A006519, A007949, A062153, A065332, A065333, A065334.

Programs

Mathematica

a[n_] := If[n/2^IntegerExponent[n, 2]/3^(e = IntegerExponent[n, 3]) == 1, e, 0]; Array[a, 100] (* Amiram Eldar, Feb 21 2021 *)

Formula

a(n) = A007949(n) * A065333(n).

a(n) = log_3(n / A006519(n)), where log_3 = A062153. For k > 0 with A065332(k) > 0: A065332(k) = (2^A065334(k)) * (3^a(k)).