That number is 36.
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The positive integer factors of 30 are: 1 2 3 5 6 10 15 30 The odd factors are therefore 1, 3, 5, 15
If you include 30, both 24 and and 30 have 8 factors, the most in that range.
28
An odd number of odd numbers can't add up to an even number.
The odd numbers between 30 and 40 are: 31 33 35 37 39