The scaling relations for the dispersion coefficients of long-range interactions between the Mu(1s)–Mu(1s, 2s, or 2p) systems and the H(1s)–H(1s, 2s, or 2p) systems are obtained using analytical properties of hydrogenic wavefunctions, which allows us to obtain the dispersion coefficients for Mu(1s)–Mu(1s, 2s, or 2p) systems from the corresponding H(1s)–H(1s, 2s, or 2p) systems. Additionally, the dispersion coefficients of long-range interactions of Mu(1s) with the ground-state H, noble gas atoms He, Ne, Ar, Kr, and Xe, alkali-metal atoms Li, Na, K, and Rb, alkaline-earth atoms Be, Mg, Ca, and Sr, and Cu, Ag, F, and Cl atoms are calculated.