A359595 - OEIS

%I #16 Jan 12 2023 18:43:51

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

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

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

%N Parity of A358777, where A358777 is Dirichlet inverse of the characteristic function of odd numbers with an even number of prime factors (counted with multiplicity).

%H Antti Karttunen, <a href="/A359595/b359595.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 a(n) = A358777(n) mod 2 = A359589(n) mod 2.

%F A353480(n) <= a(n) <= A353557(n). [See comments in A358777]

%o (PARI)

%o A353557(n) = ((n%2)&&(!(bigomega(n)%2)));

%o memoA358777 = Map();

%o A358777(n) = if(1==n,1,my(v); if(mapisdefined(memoA358777,n,&v), v, v = -sumdiv(n,d,if(d<n,A353557(n/d)*A358777(d),0)); mapput(memoA358777,n,v); (v)));

%o A359595(n) = (A358777(n)%2);

%Y Characteristic function of A359596.

%Y Parity of A358777 and of A359589.

%Y Cf. A353557.

%Y Differs from A353480 at the positions given by A359597: after 1 for the next time at n=135, where a(135) = 1.

%K nonn

%O 1

%A _Antti Karttunen_, Jan 09 2023