I've read both "up to 5" days and "5 to 6" days with the comment that the quality of the sperm drops pretty much by the 6th day. Some things one reads say longer than 6 days, but I don't know how reliable the sources were. You might google "length of life of sperm in woman's reproductive tract" and see if you can find some articles that look scientific, not just someone saying "I heard." :)
Do you happen to know how long sperm can live inside a female?
If the doctor confirmed your due date as October 2, 2013, the calculator gives you the following:
Probable date of ovulation: January 9, 2013
Possible dates of conception: January 5 to January 13, 2013
So the only date with the ex that is really significant towards trying to puzzle out paternity is January 1. I assume that was unprotected? The only reason it is even slightly possible is the long life of sperm in the woman's reproductive tract.
If you had not had sex with the guy on January 1, the January 7 event would be the only event that would be likely to produce a child due October 2. Even including the fact that you had sex with someone else on the 1st, the guy on the 7th is the most likely choice (I assume the sex was unprotected).
There are prenatal blood tests for paternity, all of which are costly, and some not reliable. The two most reliable are, naturally, the most costly. It's up to you whether you want to go that route -- if you would have the baby no matter what, and are simply curious, well, are you $1,700 to $2,100 curious? DNA tests after the baby are born are a whole lot cheaper, and are also certified by the courts.
Here are some informational links, I recommend reading both.
http://www.nytimes.com/2012/06/20/health/paternity-blood-tests-that-work-early-in-a-pregnancy.html?pagewanted=all&_r=1&
http://www.newscientist.com/article/mg20827893.200-the-danger-of-unreliable-paternity-tests.html?full=true
In any case, you will need a DNA test after the baby is born, just to be sure. In the meantime in your shoes, I would make the assumption that the second guy is the father, the one you had sex with on January 7.