Date: Thu, 19 Dec 2002 11:24:34 -0500
Reply-To: Steve Albert <salbert@AOL.COM>
Sender: "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From: Steve Albert <salbert@AOL.COM>
Subject: Re: Set statement bug?
Ed is correct, the number in the story about Ramanujan was indeed 1729.
However, let's give 729 its due:
It's the smallest number which is both a square and a cube of an odd prime.
If you sum the factors of 729 less than 729, you get 364 -- the number of
days in 52 weeks.
If you sum all the factors of 729, you get 1093, which is prime.
If you seek the two factors of 729 with the smallest sum, you get 27x27;
27+27 = 54 -- and 1093 is the 54th prime number greater than 729.
Moreover, 729 is the smallest sixth power of an integer for which this is
true. (OK, the only smaller sixth powers are 1 and 64 -- this was a pretty
easy claim to verify.)
(So, Ed, you think only you can get compulsive about numbers <g>?)