A065334 - OEIS

A065334

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

0, 1, 0, 2, 0, 1, 0, 3, 0, 0, 0, 2, 0, 0, 0, 4, 0, 1, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0

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OFFSET

1,4

COMMENTS

For k > 0 with A065332(k) > 0: A065332(k) = (2^a(k)) * (3^A065335(k)).

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..16384

Antti Karttunen, Data supplement: n, a(n) computed for n = 1..100000

FORMULA

a(n) = A007814(n) * A065333(n).

MATHEMATICA

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