A pure fusion warhead would release far less radioactive material, as the main product of fusing tritium and deuterium is simply Helium, which is not radioactive whatsoever. However, each reaction also releases a high energy neutron. These neutrons are uncharged and therefore they are very very hard to stop compared to other forms of radiation.
A neutron bomb is known as an Enhanced Radiation Weapon: An ERW is a fission-fusion thermonuclear weapon (hydrogen bomb) in which the burst of neutrons generated by a fusion reaction is intentionally allowed to escape the weapon, rather than being absorbed by its other components. The weapon's X-ray mirrors and radiation case, made of uranium or lead in a standard bomb, are instead made of chromium or nickel so that the neutrons can escape.
NORMALLY these neutrons would be captured by uranium that surrounds the fusion core. These neutrons cause a huge fission chain reaction that release much more energy than a simple fission type weapon.
MisterX is correct in that we don't use them because for the same size, the yield is much less. But this was back in the cold war where the effects of radiation and fallout were much less known. And arguably more accepted.
I understand the N bomb is somewhat safer than the a because the radiation is absorbed, but doesn't linger?
The neutrons released in the explosion penetrate the body and some collide with other molecules and atoms, knocking them out of place, ionizing them, and so forth. When a neutron strikes a DNA section it damages it. This can lead to huge amounts of cell death in high doses, or cancer in lower doses.
However the A bomb on Japan hasn't left any long lasting radiation, except in people. So its the H-bomb that is the problem, while the a and n do what they do, its only really instantly and for a short period this occurs for.
There is definitely leftover radioactive particles from the orignal two a-bombs dropped on japan. Due to cleanup and half life the amount is very low, but it is there. An EWR weapon would cause some radioactive particles to be created by neutron absorbtion and subsequent decay mechanisms, but neutrons themselves decay to protons after about 15 minutes unless inside a nucleus and aren't dangerous on their own.