After havdala we often sing "Hamavdil ben kodesh l'chol". The second line asks for forgiveness of our sins. Why is forgiveness of our sins our concern so early in the week? Does it imply we have been concerned with this all shabbat and now want to wipe the slate clean for the new week? Are our sins (individual or collective) an appropriate (or even mandated) topic of concern and reflection on shabbat?
Chassam Soffer has a Tshuva in Chelek Orach Chaim siman 67 where he says he sings this every Motzai Shabbos, but he conceded that it was originally meant to be sung on Motzai Yom Kippur, as he brings from the Mordechai at the end of Maseches Yoma. That is why there is a focus on having our sins forgiven.
Pri Tzadik Parshas Bo - page 53 discusses this at length. I will attempt to explain it to the best of my ability. Based on the Gemara in Shabbos 118b Shabbos is a time of forgiveness for sins, as one who keeps Shabbos properly, even if they did the sin of Avoda Zara, is forgiven. Motzei Shabbos where we go from a very high level to a significantly low level we pray at that time to remain pure.