Odd abundant number

An odd abundant number is an odd number $n$ 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.

Formulas

The following formula

$945+630n$ presents 62 abundant numbers, but it fails if

$n\geq 62$.

The second formula

$3465+2310n$ presents 192 abundant numbers, but fails if

$n\geq 192$

The third formula

$2446903305+1631268870n$

fails if $n\geq 135939073$.

Properties

• A 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 10³⁰.

References

This article "Odd abundant number" is from Simple English Wikipedia. The list of its authors can be seen in its historical and/or the page Edithistory:Odd abundant number.

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