Intrinsic nonlinearity Q(0)(omega) under medium amplitude oscillatory shear (MAOS) deformation was investigated for monodisperse polystyrene (PS) solutions at various concentrations, which were classified as unentangled or entangled solution in semidilute regime. These two types of PS solutions displayed different shapes when Q(0) was plotted as a function of frequency (omega). Unentangled solutions showed increases of Q(0) with frequency at the low frequency region and then plateau behavior at the high frequency region. On the contrary, entangled solutions showed an increase of Q(0) before the MAOS terminal relaxation time and a subsequent decrease, which is similar to that observed for entangled linear polymer melts. The Q(0)(omega) curves of each group were superposed in a dimensionless coordinate (Q(0)/Q(0,max) vs De), so that transition from the plateau of Q(0) to decreasing Q(0) at the high frequency region might indicate the onset of entanglement in polymer solution. In particular, all unentangled solutions had the same Q(0),(max) value (0.006) regardless of polymer concentration and molecular weight because Q(0) responds to Rouse-like relaxation process only, which is featured as no interchain interaction and chain stretching. However, the Q(0,max) values of entangled solutions were dependent on the number of entanglements (Z). The master curve of Q(0),(max) as a function of Z showed that Q(0), was constant at low entanglement numbers (few or virtually no entanglements) and then increased with the beginning of entanglement to approach a limiting value at high entanglement numbers, where reptation is the dominant linear relaxation process. In addition, the master curve of Q(0),(max) as a function of Z was used to quantify the degree of tube dilation based on the dynamic tube dilution (DTD) theory. Direct comparison of the Q(0),(max) values of semidilute solutions and melts showed that they followed the same molecular dynamics in MAOS flow like SAOS (small amplitude oscillatory shear) flow. Comparison between static and dynamic dilutions using the Q(0),(max) master curve suggested that this curve could characterize the effective number of entanglements per backbone chain for branched polymers. Because it was confirmed again that Q(0)(omega) is highly sensitive to various relaxation processes, MAOS tests may provide a new means of investigating molecular dynamics.