The mass of the alpha-particle is ~7000 times greater than that of an electron, so the velocity and hence the range of a-particles in matter is considerably less than for beta-particles of equal energy. Consequently the optimum radionuclide for medical nanorobots is predominantly an alpha emitter.
Among all gamma-free alpha-only emitters with t1/2 > 106 sec, the highest volumetric power density is available using Gd148 (gadolinium) which a-decays directly to Sm144 (samarium), a stable rare-earth isotope. A solid sphere of pure Gd148 (~7900 kg/m3) of radius r = 95 microns surrounded by a 5-micron thick platinum shield (total device radius R = 100 microns) and a thin polished silver coating of emissivity er = 0.02 suspended in vacuo would initially maintain a constant temperature T2 (far from a surface held at T1 = 310 K)
75-year half-life, initially generating 17 microwatts of thermal power which can be converted to 8 microwatts of mechanical power by a Stirling engine operating at ~50% efficiency. (Smaller spheres of Gd148 run cooler.) While probably too large for most individual nanorobot designs, such spheres could be an ideal long-term energy source for a swallowable or implantable “power pill” (Chapter 26) or dedicated energy organ (Section 6.4.4). A ~0.2 kg block of pure Gd148 (~1 inch3) initially yields ~120 watts, sufficient in theory to meet the complete basal power needs of an entire human body for ~1 century (given suitable nucleochemical energy conversion and load buffering mechanisms, and a sufficiently well-divided structure).
The last part is the punchline, of course. Freitas acknowledges future design challenges such as energy conversion, load buffering, and division of structure. If these challenges are overcome, a large block of Gd148 (or simply gadolinite ready to be processed into pure gadolinium) could supply nutrition to millions of people for millennia. Gadolinium has a half-life of 75 years, so you’d need double as much for each 75-year period you wish to avoiding refueling for, but storing gadolinium in its stable gadolinite form seems avoid this problem. Unfortunately, gadolinite is fairly rare and gadolinium itself is only found in the Earth’s crust at a 6.2 ppm level. By comparison, the abundance of gold in the Earth’s crust is only 0.0011 ppm. According to this page, annual production of gadolinium is 200 tons.
Just to throw some numbers out there, if one cubic inch is enough per person per century, a million people would require a million cubic inches. That can fit in a cube 9 x 9 x 9 ft large. According to Freitas’ numbers, this would weigh about 200,000 kg, or 200 metric tonnes, which is on par with today’s annual production. If demand for gadolinium grew, it seems plausible that its cost would fall greatly — after all, gold is about 6,000 times rarer and our annual production is 2,800 tons. Feeding ten billion people with gadolinium, if that were possible, would require about 2,000,000 metric tonnes for the first century. At an extraction rate of 200,000 metric tonnes per year, it could be done in a decade. This would require increasing current production by a factor of 1,000. According to this book, gadolinite can contain 40% rare earth oxides, 5% of which consists of gadolinium itself. That means that gadolinium makes up about 2% of the total. (Wrong: see comments.) Processing ten million metric tonnes of the ore annually would yield the required amount. For comparison, we extract 1.2 billion tons of iron from the Earth’s crust annually.
Update: all of the above is wrong for one reason or another, as pointed out in the comments, but at least I had fun. I was confusing chemical stability with nuclear stability and made the mistake that I thought gadolinium-148 would be nuclear-stable in its gadolinite form, which is wrong. The atomic number of gadolinium is 64 meaning that gadolinium-148 contains 20 extra neutrons above neutron-proton parity. It seems to me that we’d eventually have to find a less safe and cheaper isotope to make this work on a large level if it’s suitable in practice and we ever want to.