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

1,4

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 *)

Prog

(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

Crossrefs

Cf. A007814, A065332, A065333, A065335.

Sequence in context: A103775 A331594 A093057 * A356945 A162590 A276424

Adjacent sequences: A065331 A065332 A065333 * A065335 A065336 A065337

Keyword

nonn,look

Author

Reinhard Zumkeller, Oct 29 2001

Extensions

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

Status

approved