Absence of the 1/8 -anomaly in oxygen isotope effect on YBa$_{2}$Cu$_{3}$O$_{y}$

We have prepared oxygen isotope exchanged crystals of impurity-free YBCO with various oxygen concentents, and examined pure doping ($p$) dependance of isotope effect on superconducting transition temperature. With decreasing oxygen contents, the isotope exponent $alpha$ monotonously increases without any anomaly around $p = 1/8$. The monotonous increase in $alpha$ indicates that phonons are involved in the mechanism which causes the monotonous $T_c$ suppression with underdoping.