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

Offset: 1

Author

Reinhard Zumkeller, Oct 29 2001

Keywords

• nonn
• look

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

Crossrefs

Cf. A007814, A065332, A065333, A065335.

Programs

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 *)

PARI

A065334(n) = if(1==n,0,my(f = factor(n)); if(f[#f~, 1] > 3, 0, valuation(n,2))); \\ Antti Karttunen, Oct 09 2018

Formula

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

Extensions

Typo in formula corrected, erroneous comment removed by Antti Karttunen, Oct 09 2018