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a(n) = number of odd divisors of n that have an odd number of prime factors with multiplicity.
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%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