Madonna and Lionel Richie Top the Charts

This week on the pop charts, new albums by Madonna and Lionel Richie are hits, and a newfangled chart rule keeps Justin Bieber’s new single from reaching No. 1.

Madonna’s latest, “MDNA” (Interscope), sold 359,000 copies in its first week out, according to Nielsen SoundScan. That sent her to No. 1 for the eighth time — among female performers, putting Madonna second only to Barbra Streisand, who has had nine No. 1s. Madonna benefited from early promotion by performing at the Super Bowl halftime show, but her numbers this week were also helped by a promotion bundling the album with sales of her concert tickets.

Mr. Richie had his best sales week in two decades with “Tuskegee” (Mercury Nashville), which features country versions of his hits from the 1970s and ’80s, performed as duets with Nashville stars like Shania Twain, Kenny Chesney and Willie Nelson. The album sold 199,000 copies and opens at No. 2.

The music industry was closely focused this week on Madonna and Mr. Richie’s performance, and both made good impressions. But a more interesting race has been on Billboard’s Hot 100 chart, which tracks singles. That chart’s positions have long been computed through a mix of sales and airplay, but last month Billboard tweaked its formula to incorporate popularity on digital streaming services like Spotify and Rhapsody. This was the first week in which that change has affected what reaches No. 1.

“Boyfriend,” Mr. Bieber’s latest single, had a strong opening last week with 521,000 downloads; “We Are Young” by fun., which has been No. 1 for the last four weeks, had only 364,000 downloads. But since “Boyfriend” had fewer streams, that song will open at No. 2, and “We Are Young” will stay on top for another week. (“We Are Young” also had more airplay, but Silvio Pietroluongo, Billboard’s director of charts, said that the difference in streams put fun. over the top.)

Also this week, Adele’s juggernaut “21” (XL/Columbia) is No. 3 on the album chart with 121,000 sales — bringing that album’s total in the United States to 8.5 million — and Katy Perry re-entered the top 10 with an expanded reissue of her 2010 album “Teenage Dream” (Capitol), which landed at No. 7 with 33,000 sales.