William Henry Harrison, the 9th President of the US, died at the age of 68 of complications from pneumonia, which made his term in office the shortest among all the other US presidents on history. Harrison also became the first one to die in presidential office. His tenure lasted 31 days and was followed by a serious constitutional crisis, which, anyway, didn't last for a long time.

Here is the information about the other presidents in the list:

Chester A. Arthur only served about 6 months before dying in office.

Zachary Taylor served 15 months.

Warren G. Harding served 2 years and 4 months.

More Info: en.wikipedia.org