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2013-07-20, 20:35   #2
science_man_88

"Forget I exist"
Jul 2009
Dumbassville

26·131 Posts

Quote:
 Originally Posted by mart_r For example, for large enough odd sigma(n)-n, it's quite easy to find a possible n. It doesn't take long to find a prime p such that q=(sigma(n)-n-1-p) is also prime and n=p*q is found. The problem now is determining whether this is the smallest solution (mostly it isn't), and how efficiently can it be found?
Clearly I'm no expert, but I have made a script to look backwards before, that is:
y=sigma(n)-n knowing y solve for possible n so I agree solving for any n can be done simple enough ( though pari can only go so far it seems) really solving for smallest n should be possible as soon as we can limit down the amount of partitions of y that are usable ( as I have tried once they have to have properties of a list of proper divisors so primes need to be in the list or it doesn't work, 1 is a divisor of every natural so you can take it to partitions of y-1 that don't include 1,that include naturals only divisible by the primes in that partition, but don't include powers of those primes that will bring the top number to less than n ( and clearly the top prime is less than y to fit into a partition of y).