A trivial solution would be to define the function
\[CapitalPhi][m_, k_] := Cyclotomic[m, k]
Then write your comparision as
myPi[n_] := Sum[KroneckerDelta[\[CapitalPhi][m, 1], m], {m, 1, n}]
myPi[1001] == PrimePi[1001]
(* Out[505]= True *)
Copying the first line as Latex gives the string
\text{myPi}(\text{n$\_$})\text{:=}\sum _{m=1}^n \delta _{\Phi (m,1),m}
which shows up as
$$\text{myPi}(\text{n$\_$})\text{:=}\sum _{m=1}^n \delta _{\Phi (m,1),m}$$