A359832 - OEIS

%I #18 Jan 25 2023 22:23:08

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

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

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

%N a(n) = 1 if the 2-adic valuation of n is either 0 or odd, otherwise 0.

%H Antti Karttunen, <a href="/A359832/b359832.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 odd, and 0 if e is even (and > 0), with a(p^e) = 1 for all odd primes p.

%F a(n) = 1 - A328981(n).

%F a(n) = A000035(n+A048675(n)).

%F Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 5/6. - _Amiram Eldar_, Jan 24 2023

%t a[n_] := If[(e = IntegerExponent[n, 2]) == 0 || OddQ[e], 1, 0]; Array[a, 100] (* _Amiram Eldar_, Jan 24 2023 *)

%o (PARI) A359832(n) = (!(n=valuation(n,2))||(n%2));

%o (PARI) A359832(n) = { my(f=factor(n)); prod(k=1, #f~, ((2!=f[k, 1]) || (f[k, 2]%2))); };

%o (Python)

%o def A359832(n): return (n&1)|((~n & n-1).bit_length()&1) # _Chai Wah Wu_, Jan 24 2023

%Y Characteristic function of A359794.

%Y Cf. A000035, A007814, A048675, A328981 (one's complement), A359833 (Dirichlet inverse).

%K nonn,mult

%O 1

%A _Antti Karttunen_, Jan 24 2023