Why is 945 an abundant number

Notice that all those numbers are even. OEIS informs us that is the nd abundant number. The first abundant numbers are all even numbers. Wow, is the smallest ODD abundant number. OEIS also lists the first 31 odd abundant numbers. Hanover, NH: Dartmouth College, Singh, S. New York: Walker, pp. Sloane, N. Souissi, M. Karachi, Pakistan: Hamdard Nat.

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The first few abundant numbers are 12, 18, 20, 24, 30, 36, 40, 42, 48, Note that most of these appear to be even; the first odd one does not appear until This is quite remarkable, as it provides a naturally occurring example of a large number.

After , the odd-abundant numbers are 1,, 2,, 2,, 3,, There are also abundant numbers whose proper divisors have a sum greater than twice the original number. The smallest one is , but no odd ones occur until 1,,,, The first odd abundant number not divisible by 5 is. The first odd abundant number not divisible by 7 is. The first 3 -rough i. The first 5 -rough i. The first 7 -rough i. The first 11 -rough i.