1. A color correction coefficient generating apparatus comprising: a first color information obtaining unit that obtains pieces of color information to be corrected in a color space made up of a plurality of color components including a specific color component; a second color information obtaining unit that obtains pieces of color information used for correction corresponding to the pieces of color information to be corrected in the color space; a weighting coefficient obtaining unit that obtains weighting coefficients corresponding to the pieces of color information to be corrected, on the basis of a position relationship between colors represented by the pieces of color information to be corrected and a specified color region, and weights that are based on densities of the colors represented by the pieces of color information to be corrected; and a generating unit that generates color correction coefficients for correcting specific density values, by using density values of the specific color component of a plurality of the pieces of color information used for correction corresponding to a plurality of the pieces of color information to be corrected in which the specific color component has the specific density values, and a plurality of the weighting coefficients corresponding to a plurality of the pieces of color information to be corrected in which the specific color component has the specific density values.