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.