A Computerized Extension of Srinivasa Ramanujan's Tables I-III
Given in his 1916 article "On Certain Arithmetical Functions"
By Shalosh B. Ekhad
To commemorate Srinivasa Ramanujan's (1887-1920)
125-th birthday on Dec. 22, 2012, Krishna Alladi and Frank Garvan
organized an International Conference,
(see: http://www.math.ufl.edu/~fgarvan/ramanujan125.html )
where my beloved master, Doron Zeilberger gave one of the
ten plenary lectures.
His lecture was entitled: "The greatest Experimental Mathematician"
See: http://www.math.ufl.edu/~fgarvan/ramanujan125/talks/zeilberger/
He was wondering whether I can extend Srinivasa's amazing
hand calculations done in Tables I-III
of his 1916 article "On Certain Arithmetical Functions".
Ramanujan computed (by hand!) PHI[0,s] for s<=31 (Table I)
and PHI[1,s] for 1