A065332 3-smooth numbers in their natural position, gaps filled with 0.

1, 2, 3, 4, 0, 6, 0, 8, 9, 0, 0, 12, 0, 0, 0, 16, 0, 18, 0, 0, 0, 0, 0, 24, 0, 0, 27, 0, 0, 0, 0, 32, 0, 0, 0, 36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 54, 0, 0, 0, 0, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, 72, 0, 0, 0, 0, 0, 0, 0, 0, 81, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 96, 0, 0

Offset

1,2

Links

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

Formula

a(n) = if A065330(n) = 1 then n else 0.

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

If a(k) > 0 then a(k) = (2^A065334(k)) * (3^A065335(k)).

From Amiram Eldar, Sep 16 2023: (Start)

Multiplicative with a(p^e) = p^e if p <= 3, and 0 otherwise.

Dirichlet g.f.: 6^s / ((2^s-2)*(3^s-3)).

Sum_{k=1..n} a(k) ~ (n/(log(2)*log(3))) * (log(n) + log(6)/2 - 1). (End)

Mathematica

smooth3Q[n_] := n == 2^IntegerExponent[n, 2]*3^IntegerExponent[n, 3];
a[n_] := n Boole[smooth3Q[n]];
Array[a, 100] (* Jean-François Alcover, Oct 17 2021 *)

Prog

(PARI) a(n) = if(n >> valuation(n, 2) == 3^valuation(n, 3), n, 0); \\ Amiram Eldar, Sep 16 2023

Crossrefs

Cf. A003586, A065330, A065331, A065333, A065334, A065335.

Sequence in context: A322981 A232749 A181578 * A378212 A381094 A265515

Adjacent sequences: A065329 A065330 A065331 * A065333 A065334 A065335

Keyword

mult,nonn,easy

Author

Reinhard Zumkeller, Oct 29 2001

Status

approved