It seems (perhaps only to me) like it ought to factor nicely, because 20 is twice 10. But once you factor out that 10 and that 3 you’re just left with a prime, since 2010 is just 2·3·5·67. (Speaking of four primes, did you know that you can get four prime New York Steaks for $132.95 on Amazon? I was relieved to see that they were not available for Super Saver Shipping.)

Wolfram Alpha points out that 2010 itself is a factor of 29^{6}-1. And Number Gossip adds that it’s untouchable, which means that there aren’t any numbers whose proper divisors add up to 2010.

It can be written as 133122 in Base 4, which is kind of cool, and as 6, 3, 12 in Base 18; my favorite, however, is that it is 5, 10, 15 in Base 19.

Finally, it’s equal to:

669+670+671

400+401+402+403+404

127+128+…+141 and several others

[Hmmm…I can find a string for each of the 7 odd factors, but I’m not sure that exhausts all of the possibilities.]

*While getting ready to post this, I noticed that MathNotations has a similar post from yesterday. Whoops!*

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This entry was posted on January 2, 2010 at 8:58 am and is filed under Miscellaneous, Uncategorized. You can follow any responses to this entry through the RSS 2.0 feed.
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January 2, 2010 at 3:10 pm |

The number of ways a number can be written as the sum of consecutive integers equals twice the number of odd factors (subtract one if you don’t count the number itself). So 8. Or 7 if 2010 by itself doesn’t count.

Answer is not here but a description of the class is, and there are hints in the post and a rough explanation in one of the backlinks.

Jonathan

January 4, 2010 at 7:55 am |

[…] really late doing this article and it has already been done very well by MathNotations and 360. There’s also a nice game involving the number 2010 over at Let’s play math. They […]

January 7, 2010 at 12:20 am |

I thought this was pretty cool:

2010 = 1+2-(3-4-5)*6*7*8-9

which is just one of several combinations for 2010. The combination is originally from: http://www.thesamet.com/2010.txt. Check out that site for several other variations.

January 8, 2010 at 10:02 pm |

[…] week discussing fascinating facts about the number 2010. Check out the posts at MathNotations and 360. I read about this gem: 2010 = […]