Most large numbers can't be factored into nearly equal factors, if we take "nearly equal" to mean "differ by less than a factor of two". I called these "puzzle

Most large numbers can't be factored into nearly equal factors, if we take "nearly equal" to mean "differ by less than a factor of two". I called these "puzzle numbers" because they're reasonable numbers of pieces for a jigsaw puzzle to have, and wrote about it a couple years ago: https://gottwurfelt.com/2020/08/17/how-many-pieces-can-a-puzzle-have/ https://gottwurfelt.com/2020/08/17/how-many-pieces-can-a-puz... For example you could have a 299-piece puzzle (13 by 23) or a 300-piece puzzle (15 by 20) but not a 301-piece puzzle (this will only factor as 7 by 43, which is an odd shape for a puzzle). Unsurprisingly such numbers were in the OEIS (and I didn't put them there): https://oeis.org/A071562 https://oeis.org/A071562.