(1, 3, 5, 7, 9, 15, 21, 25, 27, 35, 45, 63, 75, 81, 105, 135, 175, 189, 225, 315, 405, 525, 567, 675, 945, 1575, 2025, 2835, 4725, 14175)>>Total==30 such numbers
10! = 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 =
(5 * 2) * (3 * 3) * ( 4 * 2) * 7 * (3 * 2) * 5 * (2 * 2) * 3 * 2 =
(5 ) * (3^2) * 7 * 3 * 5 * 3 =
3^4 * 5^2 * 7^1
The number of odd divisors = add 1 to each exponent ...take the product of these sums = (4 + 1)(2 + 1) (1 + 1) = (5) (3) ( 2) = 30
(Just as the Guest said !!! )