On Kassel-Reutenauer q-analog of the sum of divisors and the ring F3[X]/X2F3[X]

A q-analog Pn(q) of the sum of divisors of n was introduced by C. Kassel and C. Reutenauer in a combinatorial setting and by T. Hausel, E. Letellier, F. Rodriguez-Villegas in a Hodge-theoretic setting. We study the reduction modulo 3 of the polynomial Pn(q) with respect to the ideal (q2+q+1)F3[q].