The candela is odd.
The candela is a measure of human perceived brightness. As people's perception of the brightness of a light source depends on the wavelength of the light (we are most sensitive to wavelengths corresponding to green (around 550nm) and less efficient to shorter and longer wavelength) the definition of the candela has to include a multiplier representing the relative luminous efficiency as a function of wavelength - this function is known as V-lambda. The definition of V-lambda is based on people subjectively matching the brightness of lights with different wavelengths. The standard V-lambda defined by the CIE (Commission Internationale de l'Éclairage) is, in fact, based on measurements from a very small number of observers. There are different versions of V-lambda for daylight adapted (photoptic) vision, dark adapted (scotopic) vision, and the intermediate state - mesopic vision. The candela is defined in terms of the physical power of a light over an illuminated area at a single standard wavelength (and so is entirely physical at that wavelength), but to use the candela as a measurement of luminous intensity at any other wavelength one has to use a subjectively defined multiplier from the appropriate V-lambda. All pretty weirdly subjective for an SI base-unit!
(I study human vision for a living.)