Was the original idea for the book based on a Dimension X radio show?
Pebble in the Sky, written by Isaac Asimov
https://www.youtube.com/watch?v=r60fsJct0oY
Pebble in the Sky
Year: 1951
Duration: 30 min
Genre: Future Earth
Story by: Isaac Asimov
Awards: Hugo (retro, nom), 2001
A radioactive and decrepit Earth prepares in secret for a deadly gambit to reclaim its prodigal colonies and rebuild its galactic empire.
As you can see, the stories are completely different, but one of the plot points in Pebble in the Sky was 'the 60': that all humans were killed when they were 60 years old. The reasoning was different, as in the Pebble in the Sky it was based on the idea that too many people would consume too many resources.
I realize that writers can come up with the same idea completely independently, but they also frequently copy from each other.