If you want to avoid the sugar, add orange juice in place for a little extra zing.
Preheat oven to 450F.
Prick potatoes and bake in the middle of the oven for 1 ½ hours, or until very soft. Scoop flesh into a bowl.
In a saucepan cover apricots by 1-inch with cold water and simmer until soft, about 30 minutes. Reserve 2 tablespoons cooking liquid and drain apricots. In a food processor, puree apricots with sugar and reserved liquid until smooth.
Add puree to potatoes with salt to taste and beat with an electric mixer until smooth. Spread into butter 2-qt shallow baking dish. Pure may be prepared 1 day ahead and chilled covered.
Reduce oven to 400F.
In a small bowl blend with your fingers flour, brown sugar, pecans and salt to taste until combined well and crumble over puree. Bake in the middle of oven until heated through and streusel is bubbling, about 15 minutes.