All unitary perfect polynomials over F2F2 with at most four distinct irreducible factors

A polynomial A∈F2[x]A∈F2[x] is unitary perfect if and only if A=∑d∣A,gcd(d,A/d)=1d. We find all unitary perfect polynomials of the form P1a1P2a2P3a3P4a4 where P1,…,P4∈F2[x]P1,…,P4∈F2[x] are irreducible polynomials and a1,…,a4a1,…,a4 are non-negative integers.