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Sequence o' Fun (Posted on 2006-01-25) Difficulty: 4 of 5
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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Solution Puzzle Solution Comment 4 of 4 |
(In reply to Answer by K Sengupta)

An integer n is an abundant number if the sum of the proper divisors of n is more than itself, in other words:  the sum of all the divisors is more than 2*n .

We observe that the given sequence consists of the abundant numbers.

For example, the positive divisors of 24 (inclusing 1 and itself) are:
1,2,3,4,6,8,12,24, and summing these divisors, we have: 60, which is greater that 2*24= 48

Thus, 24 is an abundant number. In a similar manner, it can be verified that all the other terms are indeed abundant numbers.

Checking all the odd numbers, 1,3,5,7,... in turn for this property, we observe that for 945, we observe that the sum of the divisors of 945 is greater than 1890.

Consequently, 945 is the first odd number with this property.


  Posted by K Sengupta on 2008-11-18 23:55:18
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