A monic polynomial is a single-variable polynomial in which the coefficient of highest degree is equal to 1.
Define to be the set of all monic polynomials with integer coefficients (including the constant polynomial ). A polynomial is cyclogenic if there exists and a positive integer such that . If is the smallest such positive integer then is -cyclogenic.
Define to be the sum of all -cyclogenic polynomials. For example, there exist ten 6-cyclogenic polynomials (which divide and no smaller ):