FIXED POINTS OF THE SUM OF DIVISORS FUNCTION ON F2[x]

We work on an analogue of a classical arithmetic problem over polynomials. More precisely, we study the fixed points F of the sum of divisors function sigma : F-2[x] -> F-2[x] (defined mutatis mutandi like the usual sum of divisors over the integers) of the form F := A(2) center dot S, S square-free, with omega (S) <= 3, coprime with A, for A even, of whatever degree, under some conditions. This gives a characterization of 5 of the 11 known fixed points of sigma in F-2[x].