Linear mono- and polydisperse homopolymer melts have been investigated with Fourier transformation rheology (FT rheology) to quantify their nonlinear behavior under oscillatory shear via mechanical higher harmonics, i.e., I-3/1(omega,gamma(0)). Master curves of the zero-strain nonlinearity, (3)Q(0)(omega) equivalent to lim(gamma 0 -> 0) I-3/1/gamma(2)(0), have been created for these linear homopolymer melts, applying the time-temperature superposition (TTS) principle. The quantity (3)Q(0)(omega) is examined for its dependence on molecular weight, molecular weight distribution, and monomer. The investigated nonlinear master curves of (3)Q(0)(omega) for polymer melts with a polydispersity index (PDI) of about 1.07 or smaller display the expected scaling exponent of (3)Q(0)(omega) proportional to omega(2) at low frequencies until a maximum, (3)Q(0,max), is reached. This maximum (3)Q(0,max) was found to be in the magnitude of the longest relaxation time tau(0) and the value of (3)Q(0,max) to be weakly dependent on molecular weight, or the number of entanglements Z, with (3)Q(0,max) proportional to Z(0.35). Within the measured experimental window, the initial slope at low frequencies of nonlinear master curves is very sensitive toward the molecular weight distribution, as quantified through the PDI. The slope of (3)Q(0)(omega) decreases until approximately zero as a limiting plateau value is reached at a polydispersity of around PDI approximate to 2. The experimental findings are also compared to (3)Q(0)(omega) predictions from pom-pom and molecular stress function (MSF) constitutive models. Analytical solutions of (3)Q(omega,gamma(0)) for diminishing small strain amplitudes (gamma(0) -> 0) are presented for each model, and an asymptotic solution for (3)Q(0)(omega) is derived for low and high frequencies for monodisperse samples. This simplified equation is a function of Deborah number (De = omega tau(0)) in the general form of (3)Q(0)(De) = aDe(2)/(1 + bDe(2+k)). This equation was fitted to our experimental data of monodisperse homopolymer melts. It is shown that under these conditions the parameters a and b are only functions of the number of entanglements. Z and are independent of the investigated monomers. Consequently, a and b can be linked to general polymer properties. With this article, the mechanical nonlinear response of linear polymer melts with regard to molecular weight and distribution as well as monomer type is quantified. The here presented results should be of great interest toward constitutive model development and toward computational polymer physics, e.g., molecular dynamic simulations, as our results seem to quantify general features in nonlinear rheology of linear homopolymer melts.