Are there any odd abundant numbers

Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. Prove no odd number can be abundant. Ask Question. Asked 6 years, 10 months ago. Active 6 years, 10 months ago. Viewed times. Finch, S. Cambridge, England: Cambridge University Press, pp. Guy, R. Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. Kobayashi, M. Hanover, NH: Dartmouth College, Singh, S. New York: Walker, pp.

Sloane, N. Souissi, M. Karachi, Pakistan: Hamdard Nat. Wall, C. 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. 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,,,, Googology Wiki Explore. Exponentiated linear omega level Exponentiated polynomial omega level Double exponentiated polynomial omega level Triple exponentiated polynomial omega level Iterated Cantor normal form level Epsilon level Binary phi level Bachmann's collapsing level Higher computable level Uncomputable numbers.