Odd abundant number

An odd abundant number is an odd number [math]\displaystyle{ n }[/math] that its sum-of divisors greater than the twice of itself.

Examples

The first example is 945 (3³× 5× 7). Its prime factors are 3, 5, and 7. The next following eleven odd abundant numbers are

1575, 2205, 2835, 3465, 4095, 4725, 5355, 5775, 5985, 6435, 6615.

Odd abundant numbers below 500000 are in On-Line Encyclopedia of Integer Sequences A005231.

The following formula

[math]\displaystyle{ 945+630n }[/math]^[1] presents 62 abundant numbers, but it fails if

[math]\displaystyle{ n\le62 }[/math].

The second formula

[math]\displaystyle{ 3465+2310n }[/math]^[2] presents 192 abundant numbers, but fails if

[math]\displaystyle{ n\le192 }[/math]

The third formula

[math]\displaystyle{ 2446903305+1631268870n }[/math] ^[3]

fails if [math]\displaystyle{ n\le135939073 }[/math].

An calculation was given by Iannucci shows how to find the smallest abundant number not divisible by the first n primes.
An abundant number with abundance 1 is called a quasiperfect number, although none have yet been found. A quasiperfect number must be an odd square number having a value above 10^{30^.}