Nah the 13 in the song has nothing to do with the unlucky part. It's just that the song is a goofy ass song lol. The lyrics literally start with "ding dong ding ding dong ding dong". It's basically a woman asking her lover or whatever to come home (not in the ding dong part of course).
She's like, "I waited 1, 2, 3 - 13 days" for you and you didn't come. On the 14th day, I did this, on the 15th I did this, on the 17th I realized we broke up, my heart shattered on the 20th and so on. Many find the song nostalgic (not me, cuz I'm not from that generation). For me it's just another old random annoying-ish Bollywood song.
Also, just to add to my previous comment a little with a live example here:
Kazaxat's (the person whose comment you replied to) parents are Malayali. They're from the south Indian state of Kerala. See how Kazaxat doesn't speak Hindi? Kerala is one of the states resisting Hindi imposition. Also remember how I said that the land of modern India was never under one state? Kerala was one of the lands never under the rule of any state in the Ganga basin.
Also, the actress dancing in the song above is Madhuri Dixit, who is Marathi.
Here's a link to the song if you've suddenly become curious lol. Disclaimer: it's just another silly old Bollywood song. So if u'r not into that, u ain't missing anything.