Definition coPrimeBeta (z c : nat) : nat := S (c * S z).

(* Specifications: *)
Lemma coPrimeSeq :
forall c i j n : nat,
Divides (factorial n) c ->
i <> j -> i <= n -> j <= n -> CoPrime (coPrimeBeta i c) (coPrimeBeta j c).
Lemma gtBeta : forall z c : nat, coPrimeBeta z c > 0.
Definition maxBeta (n : nat) (x : nat -> nat) : nat.