Let M(x) denote the median largest prime factor of the integers in the
interval [1,x]. We prove that
M(x)=xeβ1βexp(βlifβ(x)/x)+OΟ΅β(xeβ1βeβc(logx)3/5βΟ΅) where lifβ(x)=β«2xβlogt{x/t}βdt. From this, we obtain the asymptotic
M(x)=eeβΞ³β1βxeβ1β(1+O(logx1β)), where Ξ³ is the Euler Mascheroni constant. This answers a
question posed by Martin, and improves a result of Selfridge and Wunderlich.Comment: 7 page