2200 =(1, 2, 4, 5, 8, 10, 11, 20, 22, 25, 40, 44, 50, 55, 88, 100, 110, 200, 220, 275, 440, 550, 1100, 2200) >>Total = 24 divisors.
1, 5, 11, 25, 55, 275 = 6 odd divisors(factors), including 1.
I think the smallest odd integer with 9 divisors(factors) is:
2^2 x 5^2 =225 =(1, 3, 5, 9, 15, 25, 45, 75, 225) >>Total = 9 divisors(factors)