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