33 is the largest positive integer that can not be expressed as a sum of different triangular numbers. It is also the smallest odd repdigit that's not prime (unless we consider 1-digit integers to also be repdigits).
33 is the eighth distinct biprime comprising the prime factors (3.11). Its aliquot sum is 15; itself a discrete biprime (3.5) in the following Aliquot sequence 33,15,9,4,3,1,0. (Note 33 is the 8th composite number to descend into the prime number 3, the others outside of this sequence being 30,26,16,12)
The sum of the first four factorials is 33. Adding up the sums of divisors for the 1 through 6 yields 33. 33 is the smallest integer such that it and the next two integers all have the same number of divisors.
It is also the first member of the first cluster of three biprimes (33,34,35); the next such cluster is (85,86,87).
5 comments:
Happy Birthday!!!
What?
Sorry, I would explain why I wished Sandy, Happy birthday on J-rad's blog... several days late, but it would be a long and lame story which would only go to prove to a larger degree, what a nutball I am.
So just live with it.
It has to do with Fatigue.
Sorry The Mop, my "What?" comment was not to your birthday wishes, but rather to Jared's ridiculously nerdy explanation of the number 33. I'm so confused I've not even tried to finish reading it, and I'm just waiting for a new post so I am not lost at my friends' various web logs and such. Hope that clears it up. Wish you were still writing...
Jradness, Happy belated b-day! Obviously your blog on 33 is just your way of avoiding the fact that your get'n real old. Enjoy it while you can, before long you'll be looking down the barrel at 39, not a pretty sight.
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