* Prosieben could enter DAX in September
* Shares sold at 34.75 euros apiece
* Prosieben shares trade above placement price (Recasts with DAX entry, adds detail, background, quote)
By Arno Schuetze
FRANKFURT, Jan 17 (Reuters) - Buyout groups KKR and Permira have sold their remaining stake in German broadcaster ProsiebenSat.1, potentially paving the way for its inclusion in the country's blue chip DAX index later this year.
The private equity firms reaped proceeds of 1.26 billion euros ($1.7 billion) from the sale of their combined 17 percent stake, which was placed with unnamed investors at 34.75 euros a share, completing their gradual exit.
Prosieben shares traded at 35.10 euros by 0900 GMT on Friday, a premium to the placing price. Traders said investors were speculating the broadcaster - whose shares are now 100 percent in free float - could join the DAX later this year.
ICF index specialist Klaus Stabel said Prosieben could replace mining group K+S in the September review of the DAX's composition, adding that the broadcaster's market capitalisation and trading liquidity had been too low for a fast-track inclusion in March.
KKR and Permira in 2006 bought a controlling stake in ProSieben and merged it with SBS Broadcasting, a media group they had acquired a year earlier. Since then they have been disposing of their investment in stages.
ProSieben shares have advanced 47 percent over the last 12 months, outperforming a 41 percent gain in the STOXX Europe 600 Media index.
In October, Prosieben raised its 2015 sales goal, banking on further rapid growth in digital entertainment. ProSieben is benefiting from encouraging customers of its television services to also use its digital businesses, which include online videos, games, music and fan communities on social network sites, and vice-versa.
With consumers increasingly using smartphones and tablet computers to watch videos and listen to music, broadcasters such as ProSieben and its rival RTL Group are expanding their online media offerings to win viewers.
The stock was placed by bookrunners Deutsche Bank and Bank of America Merrill Lynch. ($1 = 0.7352 euros) (Reporting by Arno Schuetze; Additional reporting by Kirsti Knolle; Editing by David Holmes)