Odd abundant number

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An odd abundant number is an odd number that its sum-of divisors greater than the twice of itself.

Examples[change | change source]

  • 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[change | change source]

The following formula

[1] presents 62 abundant numbers, but it fails if

.

The second formula

[2] presents 192 abundant numbers, but fails if

The third formula

[3]

fails if .

Properties[change | change source]

  • 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 1030.

References[change | change source]

  1. "More Odd Abundant Sequences" (PDF). JAY. SCHIFFMAN. 2005. Retrieved 2017-01-2. Check date values in: |accessdate= (help)
  2. "More Odd Abundant Sequences" (PDF). JAY. SCHIFFMAN. 2005. Retrieved 2017-01-26.
  3. "More Odd Abundant Sequences" (PDF). JAY. SCHIFFMAN. 2005. Retrieved 2017-01-26.