The 62-year-old took to micro-blogging website Twitter to remember the legendary composer, who is known for evergreen songs like "Yaadon ki baraat", "Tum bin jaaun kahan".
"Happy Birthday Pancham! Will always miss you," Rishi tweeted along with a black and white photograph of himself along with the legendary composer.
R.D. Burman had composed several of the popular songs sung by Lata Mangeshkar, Mohammed Rafi, Asha Bhosle and Kishore Kumar.
The composer died in January 1994.