what was the number 1 song june 29th 2013

The number 1 song on June 29, 2013 on the Billboard Hot 100 was “Blurred Lines” by Robin Thicke featuring T.I. and Pharrell.

If you meant a different chart, such as the UK singles chart, the answer would be different; for example, the UK number one around that date was “I Love It” by Icona Pop featuring Charli XCX.