Talk:Highly abundant number

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Mathematics grading: Start Class Low Importance  Field: Number theory

[edit] Five and Seven

Are 5 and 7 highly abundant? I never heard of highly abundant numbers before reading this, so maybe I don't understand, but how as I understand this σ(4)=3 and σ(prime)=1.-- Randall Bart <wiki@randallbart.com> 05:08, 21 October 2006 (UTC)

I'm fairly certain there are no highly abundant primes above 3, since for any prime p, σ(p) = p+1, and since p-1 (for any prime greater than 3) is an even integer, it will always have divisors: 1,2, some integer k,itself, and maybe more. so since (p-1)+1+2 > p+1, there shouldn't be any more primes in this sequence. --habitue 06:42, 8 February 2007 (UTC)

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