%I #14 Jan 08 2025 18:35:27
%S 0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0,0,
%T 0,0,1,0,0,0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,0,0,0,0,1,0,1,0,0,0,0,0,1,0,
%U 0,0,1,0,1,0,0,0,0,0,1,0,1,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0,0,0,0,0,0,1
%N a(n) = 1 if n is an odd number with an odd number of distinct prime factors, otherwise 0.
%H Antti Karttunen, <a href="/A353673/b353673.txt">Table of n, a(n) for n = 1..65537</a>
%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>
%F a(n) = A000035(n) * A092248(n).
%F a(n) = A000035(n) - A353675(n).
%F a(n) = A092248(n) - A353674(n).
%e n = 9 = 3^2 is an odd number with an odd number of distinct prime factors, therefore a(9) = 1.
%e n = 105 = 3*5*7 is an odd number with an odd number of distinct prime factors, therefore a(105) = 1.
%t Table[If[OddQ[n]&&OddQ[PrimeNu[n]],1,0],{n,150}] (* _Harvey P. Dale_, Jan 08 2025 *)
%o (PARI) A353673(n) = ((n%2) && (omega(n)%2));
%Y Characteristic function of A098903.
%Y Cf. A000035, A001221, A092248, A353672, A353674, A353675.
%Y Differs from A174275 for the first time at n=105, where a(105) = 1, while A174275(105) = 0.
%Y Cf. also A353558.
%K nonn
%O 1
%A _Antti Karttunen_, May 03 2022