%I #9 Jan 24 2024 21:27:06
%S 0,0,1,0,1,1,1,0,1,1,1,1,1,1,2,0,1,1,1,1,2,1,1,1,1,1,2,1,1,2,1,0,2,1,
%T 2,1,1,1,2,1,1,2,1,1,3,1,1,1,1,1,2,1,1,2,2,1,2,1,1,2,1,1,3,0,2,2,1,1,
%U 2,2,1,1,1,1,3,1,2,2,1,1,2,1,1,2,2,1,2,1,1,3,2,1,2,1,2,1,1,1,3,1,1,2,1,1,4
%N a(n) = number of odd divisors of n that have an odd number of prime factors with multiplicity.
%H Antti Karttunen, <a href="/A369258/b369258.txt">Table of n, a(n) for n = 1..65537</a>
%F a(n) = Sum_{d|n} A353558(d).
%F a(n) = A001227(n) - A369257(n).
%e Of the eight odd divisors of 105, the four divisors 3, 5, 7, 105 all have an odd number of prime factors (A001222(d) is odd), therefore a(105) = 4.
%t Array[DivisorSum[#, 1 &, And[OddQ[#], OddQ@ PrimeOmega[#]] &] &, 120] (* _Michael De Vlieger_, Jan 24 2024 *)
%o (PARI)
%o A353558(n) = ((n%2)&&(bigomega(n)%2));
%o A369258(n) = sumdiv(n,d,A353558(d));
%Y Inverse Möbius transform of A353558.
%Y Cf. A001227, A067019, A369257.
%K nonn
%O 1,15
%A _Antti Karttunen_, Jan 24 2024