Why did the B-52 never have a JT4A-powered version? All versions of the B-52 use the Pratt &amp; Whitney JT3C turbojet (except for the last version, the B-52H, which uses the JT3D low-bypass turbofan instead).

Problem: the JT3C is a horribly anemic engine, especially the early versions used on the A-E (producing a mere 44.5 kN per engine on the B-52A, increasing only to 46.7 kN/engine on the B-E models).  The engines used on the F and G did better, but still topped out at 61.2 kN each.  Due to this low engine thrust, the A through G models of the B-52 all required the use of water injection (with the associated weight and space penalties) to augment their engines' thrust for takeoff, without which the aircraft would have been incapable of becoming airborne.

For this reason, the other major users of the JT3C (the 707 and DC-8 airliners) promptly switched over to the more powerful JT4A turbojet when it (the JT4A) came on the market; the JT4A provided up to 77.8 kN of thrust, allowing the JT4A-engined versions of these aircraft to do away with the heavy and complicated water-injection system.

In contrast, the B-52 never switched over to the JT4A, even though, as a heavy bomber aircraft stuffed to the gills with fuel and ordnance, it would have benefited even more from the added engine power than the airliners did.

Why did the B-52 stick to the JT3C (until they finally jumped ship for the JT3D), and not go for the JT4A when it became available?
The military designation of the proposed JT4A is J75 (not to be confused with J57).
It was proposed for the G-variant of the B-52, but it would have slowed down the production:

The B-52G was proposed to extend the B-52's service life during delays in the B-58 Hustler program. At first, a radical redesign was envisioned with a completely new wing and Pratt &amp; Whitney J75 engines. This was rejected to avoid slowdowns in production, although changes were implemented. The most significant of these was the brand new &quot;wet&quot; wing (...)
—livingwarbirds.com

Even a simple re-engine (as opposed to re-wing and re-engine) takes a lot of resources and time. The new engines are about 10% heavier, and they would need new nacelles, aerodynamic and flutter testing, etc. So, it was considered, but it wasn't the right time – fast production was needed for its role in the Cold War; 193 B-52Gs were delivered 1959–1961, making it the most produced variant.