This paper studies numerically the Weeks-Chandler-Andersen (WCA) system,
which is shown to obey hidden scale invariance with a density-scaling exponent
that varies from below 5 to above 500. This unprecedented variation makes it
advantageous to use the fourth-order Runge-Kutta algorithm for tracing out
isomorphs. Good isomorph invariance of the structure and dynamics is observed
over more than three orders of magnitude temperature variation. For all state
points studied, the virial potential-energy correlation coefficient and the
density-scaling exponent are controlled mainly by the temperature. A mean-field
theory is presented based on the assumption of statistically independent pair
interactions, which rationalizes this finding
