$exp(i2\pi px/a)$ with p an integer is periodic with period a while $exp(ip'x'/\hbar)$ is not periodic.

when the former is taken as the basis of a Fourier transformation, there comes the factor $a$ in the Fourier expansion coefficients, while when the former is taken as the basis of a Fourier transformation,, there comes the factor $2\pi\hbar$.