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 $p=1\mathrm{/}8$. The monotonous increase in $\alpha$ indicates that phonons are involved in the mechanism which causes the monotonous $T_c$ suppression with underdoping.