“I realize it may vary based on the amount of stories. Perhaps there is an equation that takes into account the amount of stories.”
Um, yes, definitely. There are dozens of equations. But there is waaaaay more to it than that.
The answer to this question depends on a number of factors. Namely, as you mentioned, the height or number of stories of the superstructure, the subsurface soil conditions, the type of construction (steel or concrete), local surroundings, even how you define the term “skyscraper”...
Most “skyscrapers” will require the driving of many deep piles. Often hundreds of them to a depth of hundreds of feet deep. This task alone can take months. If it is a short skyscraper, the time to drive the piles can easily exceed the time to build the superstructure. However, in a shorter “skyscraper”, it is possible that the pile-driving task will exceed the superstructure construction.
In general, however, I don’t think this rule holds up. A recent skyscraper in San Francisco, the One Rincon, Tower One, rises 60 stories to a height of about 650ft. For the bulk of the superstructure construction, the concrete subcontractor was making 3-day floor cycles, meaning that every three days they installed reinforcing and placed the concrete for one floor. I think this was their peak production rate, and it is entirely likely that the early floors went much slower, as did the completion of the roof, as both of these areas are irregular, while the middle floors are all identical plates (more or less). Nonetheless, if we assume that they were able to complete two floors per week, then it took thirty weeks to complete the concrete core. I know that the exterior glazing and cladding also lagged the concrete considerably, so I think it’s fair to say that the “superstructure” took close to a year to complete. I have a very difficult time believing that the foundation took this long, though it is possible.
Keep in mind that this is not considered a tall skyscraper, either. The tallest buildings in San Francisco are about 25% taller than this one. New York and Los Angeles both have buidings twice as tall as this, and Chicago has even taller buildings still.
And here’s the kicker, One Rincon, being a residential condo building, had to be concrete for a variety of reasons related to residential construction, whereas most of these taller offices are steel superstructures. Steel is considerably slower to erect than concrete. As such, I believe most of the tallest skyscrapers took considerably longer to complete the super- as opposed to the sub-structure.