This might be a Swedish thing since our way of talking about work-related stuff, vacations, etc, is very much focused around week numbers.
However, I just figured out how to include week numbers in the date picker which was a feature request by an end user who does a lot of planning work:

Just add this as a script when configuring the timestamp attribute inside a form:
config.config.weekNumber = true;
Add some CSS if you like:
/*date picker display week number*/
.k-calendar .k-content .k-alt{
font-weight:bold;
font-size:10px;
}
It seems to work really well with the Swedish way of counting week numbers (yes, there are different ways to do it around the world). Maybe the locale culture settings fixes this automatically.