Let S_N(s) = sum_(n = 1)^∞ [(n^(1/N))]^(-s), where [x] denotes nearest integer function, i.e., the integer closest to x. For s>3, S_2(s) | = | 2ζ(s - 1) S_3(s) | = | 3ζ(s - 2) + 4^(-s) ζ(s) S_4(s) | = | 4ζ(s - 3) + ζ(s - 1). S_N(n) is a polynomial in π whose coefficients are algebraic numbers whenever n - N is odd.