The partition function for atoms in a gas with partial ionization is obtained by assuming that the internal and atomic linear energy densities are equal, and considering that the kinetic energy per degree of freedom is sufficient to ionize the upper levels of the atoms, and, at the same time, approximating the sum by an integral, which we solve using the mean value theorem for integrals. The resulting function reproduces the behavior of the partition function in the region of validity of perfect gases; it is also analytic and compact.