Milairjunkie has it.
Piasecki changed its name to Vertol in 1955, Frank Piasecki having left the company after a dispute, going on to form the Piasecki Aircraft Corporation that still exists working on a range of innovative designs in helicopter, UAV and other forms of aerostat development. They are also a major supplier of ovens for airliner galleys.
Vertol was bought out by Boeing in 1960. Nicole Piasecki, Frank Piasecki's daughter, is vice president of Business Development & Strategic Integration for Boeing Commercial Airplanes.
The Pratt and Whitney powered YH-16 and Allison powered YH-16A were the largest helicopters built up until then, matching the fuselage capacity of a number of current transports and generating great interest in both the US Army and Air Force.
There were plans for a 68 seater H-16B Turbotransporter but all further development ceased when the YH-16A broke apart in the air in December 1955 due to a rear rotor shaft failure.
F-8fanatic: There were, according to a number of sources, 704 H-21s were built, there were also 13 Model 44A commercial versions built.
The H-25/HUP Retriever was a little different. Many sources state 339 airframes across the range were built but the H-25 as delivered to the US Army, Canada and France was significantly different in airframe structure to the Retriever, enough to make it a separate type..
The figures are also confusing. Many internet sites stating the 339 airframes across the types, give the following:
XHUP-1 2
HUP-1 32
HUP-2 165
HUP-2S 20
HUP-3 50
H-25A 70
Total 339
I believe this total to be wildly inaccurate due to double counting of transferred and converted airframes. The 50 HUP-3s were built as model H-25A, delivered to the Army as part of the 70 ordered, 50 were transferred to the Navy when the Army found the type unsuitable. This brings the total down to 289.
The 20 HUP-20 were conversions from the HUP-2 batch and were part of the 165 ordered. This reduces the total HUP/H-25 airframes to to 269. Take off the 70 H-25A and you are left with 199 HUP airframes.
My rather pedantic "though one type was produced in the hundreds" referred to the H-21, which though produced with various engines, remained a standard airframe.
Finally, the reference to "Not airships, though the manufacturer did do something odd in this area" alluded to the PA-97 Helistat