A359834 - OEIS

%I #11 Jan 26 2023 12:17:25

%S 1,1,1,1,1,1,1,0,0,1,1,1,1,1,1,1,1,0,1,1,1,1,1,0,0,1,0,1,1,1,1,1,1,1,

%T 1,0,1,1,1,0,1,1,1,1,0,1,1,1,0,0,1,1,1,0,1,0,1,1,1,1,1,1,0,0,1,1,1,1,

%U 1,1,1,0,1,1,0,1,1,1,1,1,0,1,1,1,1,1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,1,1,1,0,1,1,1,0,1,1,1,1,1,1,1,1,0,1,1,0,0

%N Parity of Dirichlet inverse of A359832, where A359832(n) = 1 if the 2-adic valuation of n is either 0 or odd, otherwise 0.

%H Antti Karttunen, <a href="/A359834/b359834.txt">Table of n, a(n) for n = 1..100000</a>

%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>

%F Multiplicative with a(2^e) = 1 if e is not a multiple of 3, otherwise 0, and for odd primes p, a(p^e) = 1 if e = 1, otherwise 0.

%F a(n) = A359833(n) mod 2.

%F Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 52/(7*Pi^2) = 0.752671... . - _Amiram Eldar_, Jan 25 2023

%t f[p_, e_] := If[e == 1, 1, 0]; f[2, e_] := If[Divisible[e, 3], 0, 1]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Jan 25 2023 *)

%o (PARI) A359834(n) = { my(f = factor(n)); prod(k=1, #f~, if(2==f[k, 1], !!(f[k, 2]%3), (1==f[k, 2]))); };

%Y Cf. A359831, A359832.

%Y Cf. also A359590.

%K nonn,mult

%O 1

%A _Antti Karttunen_, Jan 25 2023