That is such a difficult question!!! I'll attempt an answer but I welcome comments from anyone else on this subject! Also, please let me know if you spot any mistakes and I'll amend the list!
These figures are based on albums and singles officially released by EMI/Apple, and so include Beatles at the BBC and Anthology albums. Tony Sheridan, Decca Auditions and Star Club sessions are not included in this list unless they appear on Anthology One. I have not included out-takes or live recorded versions, so, for example, Yesterday appears only once, depite its appearance as an out-take and live version on Anthology. Hope this makes sense!
Here goes!!!
Total number of tracks released = 287*
Total number of tracks written and recorded by The Beatles = 210**
Lennon/McCartney = 171***
Harrision = 25
Starkey = 2
Lennon/McCartney/Harrison/Starkey = 4****
Lennon/McCartney/Starkey = 1
Harrison/Lennon = 1
McCartney/Harrison = 1
Lennon = 1
McCartney = 4
*