A318666 - OEIS

%I #23 Jun 25 2024 12:23:10

%S 1,1,2,1,1,2,1,1,4,1,1,2,1,1,2,1,1,4,1,1,2,1,1,2,1,1,8,1,1,2,1,1,2,1,

%T 1,4,1,1,2,1,1,2,1,1,4,1,1,2,1,1,2,1,1,8,1,1,2,1,1,2,1,1,4,1,1,2,1,1,

%U 2,1,1,4,1,1,2,1,1,2,1,1,16,1,1,2,1,1,2,1,1,4,1,1,2,1,1,2,1,1,4,1,1,2,1,1,2

%N a(n) = 2^{the 3-adic valuation of n}.

%H Antti Karttunen, <a href="/A318666/b318666.txt">Table of n, a(n) for n = 1..65537</a>

%F a(n) = 2^A007949(n).

%F a(n) = A046644(n)/A317932(n).

%F Multiplicative with a(3^e) = 2^e, a(p^e) = 1 for any other primes.

%F Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 2. - _Amiram Eldar_, Nov 17 2022

%F Dirichlet g.f.: zeta(s)*(3^s-1)/(3^s-2). - _Amiram Eldar_, Jan 03 2023

%F More precise asymptotics: Sum_{k=1..n} a(k) ~ 2*n + zeta(log(2)/log(3)) * n^(log(2)/log(3)) / (2*log(2)). - _Vaclav Kotesovec_, Jun 25 2024

%t Table[2^IntegerExponent[n, 3], {n, 100}] (* _Vincenzo Librandi_, Mar 19 2020 *)

%o (PARI) A318666(n) = 2^valuation(n,3);

%o (PARI) A318666(n) = { my(f = factor(n), m=1); for(i=1, #f~, if(3 == f[i,1], m *= 2^f[i,2])); (m); };

%o (Magma) [2^Valuation(n, 3): n in [1..100]]; // _Vincenzo Librandi_, Mar 19 2020

%Y Cf. A000079, A007949, A046644, A317932.

%K nonn,mult

%O 1,3

%A _Antti Karttunen_, Sep 03 2018