RosettaCodeData/Task/Abundant-odd-numbers/00-TASK.txt

An [[wp:Abundant_number|Abundant number]] is a number '''n''' for which the   ''sum of divisors''   '''σ(n) > 2n''',
<br>or, &nbsp; equivalently, &nbsp; the &nbsp; ''sum of proper divisors'' &nbsp; (or aliquot sum) &nbsp; &nbsp; &nbsp; '''s(n) > n'''.


;E.G.:
'''12''' &nbsp; is abundant, it has the proper divisors &nbsp; &nbsp; '''1,2,3,4 <small>&</small> 6''' &nbsp; &nbsp; which sum to &nbsp; '''16''' &nbsp; ( > '''12''' or '''n'''); 
<br>&nbsp; &nbsp; &nbsp;&nbsp; or alternately, &nbsp; has the sigma sum of &nbsp; '''1,2,3,4,6 <small>&</small> 12''' &nbsp; which sum to &nbsp; '''28''' &nbsp; ( > '''24''' or '''2n''').


Abundant numbers are common, though '''even''' abundant numbers seem to be much more common than '''odd''' abundant numbers. 

To make things more interesting, this task is specifically about finding &nbsp; ''odd abundant numbers''.


;Task
*Find and display here: at least the first 25 abundant odd numbers and either their proper divisor sum or sigma sum.
*Find and display here: the one thousandth abundant odd number and either its proper divisor sum or sigma sum.
*Find and display here: the first abundant odd number greater than one billion (10<sup>9</sup>) and either its proper divisor sum or sigma sum.


;References:
:* &nbsp; [[oeis:A005231|OEIS:A005231: Odd abundant numbers (odd numbers n whose sum of divisors exceeds 2n)]]
:* &nbsp; American Journal of Mathematics, Vol. 35, No. 4 (Oct., 1913), pp. 413-422 - Finiteness of the Odd Perfect and Primitive Abundant Numbers with n Distinct Prime Factors (LE Dickson)
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