What influenced Michelangelo to make the sculpture, "The Pieta?"?

Cardinal Jean de Billheres commissioned it. Artists in Michelangelo's time worked to commission (that is, they were asked to make things by clients, and were paid for it). They never made a thing and then looked for a customer That was Michelangelo's 'influence'. There are a number of articles about it on the internet - why not start off with the wikipedia ones and then work your way down.