Certain combinatoric bernoulli polynomials and convolution sums of divisor functions

Abstract

It is known that certain convolution sums can be expressed as a combination of divisor functions and Bernoulli formula. One of the main goals in this paper is to establish combinatoric convolution sums for the divisor sums (sigma) over cap (s)(n) = Sigma(d|n) (-1)(n/d-1)d(s). Finally, we find a formula of certain combinatoric convolution sums and Bernoulli polynomials.