Ok, so I cheated to find these were the abundant numbers, but I should have recognised them. I don't usually think of them as a sequence...
Anyhow, to construct an abundant number you need a lot of factors, so it should be composed of powers of small primes. 2 is out because we need it to be odd, so I stuck with 3 and 5 at first.
3^n*5 didn't get me far, increasing n by 1 only increases the number of factors by 2. This sum climbs pretty slowly, reaching less than 80% of 3^6*5=3645
So I tried 3^n*5^m, but it does even worse.
So I added 7 to the mix.
3*5*7=105 has 87 (82.8% promising)
3^2*5*7=315 has 309 (98.1% getting warmer)
3^3*5*7=945 has 975 Got it!
Clearly this is the lowest as changing a 3 to anything else will increase the number and I tried every smaller potential number.
Posted by Jer
on 2006-01-25 14:55:47