Like most things about sleep and babies, there is no magic number of hours a 6-week-old should nap. That being said, of course you want to make sure your infant is on the right track. According to KidsHealth, a baby between the ages of 1 and 3 months is sleeping approximately 15 hours in a 24-hour period. Out of those 15 hours, about half are naps.
KidsHealth notes that most babies near the age of 6 weeks will take two to three naps per day. Most likely, you will find that your infant naps for a few hours in the mid-morning, a few more hours in the afternoon and then for a shorter period of time in the early evening; just keep in mind that not all babies follow the exact same schedule. You shouldn't worry if your 6-week-old isn't following this pattern yet.
The amount of time baby should be napping at 6 weeks of age is certainly not set in stone. Rather than worry about exactly how many hours at a time your little one should be sleeping, focus on developing a daily routine with your baby. That way, he will know what to expect each day. For instance, baby eats at 6 a.m., naps for two hours and then wakes to eat again by 8:30. Baby enjoys some awake time, then naps again until noon and feeds and so on. Of course, a regular sleep routine is something to strive for; as HealthyChildren.org points out, a newborn's sleep is often sporadic and unpredictable for the first 1 to 2 months.
If your baby seems to sleep all the time with very little awake time, you are not alone. As KidsHealth points out, young babies often snooze throughout the day, only waking to eat. The problem with this sleep scenario is that baby will often wake frequently during the night because he isn't enjoying long enough stretches of awake time during the day. Don't worry; you are not powerless to prevent another night of no sleep.
If your baby is prone to dozing off all day, try stimulating your sweetie in the morning, afternoon and early evening so he doesn't nap continuously. Talk to your tot, sing to him, give him the raspberries, bathe him, and engage him with colorful rattles and toys -- all with the goal of getting him to stay awake for longer periods of the day. The payoff is that he will learn to fall in line with your sleep schedule. Just know that this doesn't happen overnight. It takes days or even weeks for your wee one to get it. In fact, KidsHealth points to the benchmark of 4 months for when you can expect baby's sleep rhythms to become established.