14 Apr
2004
14 Apr
'04
10:01 a.m.
2. Is there a nice asymptotic expression for the number of E_n < x ???
The product of the primes <= X is (very roughly) e^X. There are about X/logX primes <= X, and their "average" magnitude is (very roughly) X. Suggested notation: We are using X# for this product. I suggest extending this to X## for the LCM of numbers <= X. This is the same as the product (for each prime) of the largest prime power <=X. So 6# = 2.3.5 = 30, while 6## = 4.3.5 = 60. The logs of X# and X## are standard functions in analytic number theory. Rich rcs@cs.arizona.edu