Talk:Abundant odd numbers: Difference between revisions

==On Number Theoretic Tasks==

Perhaps we should have a tag "This solution is lame, please make it interesting and remove this tag". RC has too many tasks which are being solved by a loop which factorize a sequence of integers and then print something based on an if condition. Better would be if the author of these tasks indicated an interesting solution in the task description based on number theory. For this task I have added a reference which proves a number of properties of Odd Abundant numbers. 3 might be of interest to this task: there are no Odd abundant numbers with fewer than 3 prime factors; if a number is odd and abundant then so too are all odd multiple of that number; and Odd abundant numbers must satisfy the condition (p1/p1-1)*(p2/p2-1)..(pn/pn-1)>2. So p1=3,p2=5 then p3 must be less than 17 because (3/2)*(5/4)*(13/12)=2.03125 and (3/2)*(5/4)*(17/16)=1.9921875. Errors in early implementations uncovered the smallest Odd abundant number not divisible by 5. Let me consider p1=3, p2=7 and p3=11. (3/2)*(7/6)*(11/10)=1.9250000000000003 so there are no Odd abundant numbers not divisible by 5 with 3 prime factors. So p1=3, p2=7, p3=11, p4=13 -> (3/2)*(7/6)*(11/10)*(13/12)=2.0854166666666667 so this is a good place to start looking. So what is the smallest Odd abundant number not divisible by 3?--[[User:Nigel Galloway|Nigel Galloway]] ([[User talk:Nigel Galloway|talk]]) 21:29, 19 May 2019 (UTC)