What is the name of a repeat of nucleotide sequences that is cut off at the end of DNA replication and acts as a counter for how many times a cell has divided.?

The repeat of nucleotide sequences that is cut off at the end of DNA replication is called a "telomere." Telomeres protect the ends of chromosomes from deterioration and prevent them from fusing with other chromosomes. Each time a cell divides, telomeres shorten, acting as a biological clock that limits the number of divisions a cell can undergo. When telomeres become too short, the cell can enter senescence or undergo programmed cell death.