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 Sequence o' Fun (Posted on 2006-01-25)
What is the first odd number of this sequence:

12, 18, 20, 24, 30, 36, 40, 42, 48, 54, 56, 60, 66...

 See The Solution Submitted by Joe Rating: 3.0000 (3 votes)

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 Smaller than I thought... (spoiler) | Comment 1 of 4

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

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