Reutenauer and Kassel introduced a family Pn(q) of polynomials defined in terms of divisors of n on overlapped intervals. The evaluation of Pn(q) at roots of unity of order 2, 3, 4, 6 form well-known integer sequences related to the number of integer solutions of the equations x2 + y2 = n, x2 + 2y2 = n, and x2 + xy + y2 = n. Also, Pn(1) is the sum of divisors of n. In this paper we define a new family Ln(q) of polynomials defined in terms of divisors of n on overlapped intervals, slightly modifying the definition of Pn(q). The values of Ln(q) at q = 1 and q = -1 are related to the sum of divisors of n and to the number of integer solutions of the equations x2 + xy + y2 = n and x2 + 3 y2 = n.
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