A summation formula for sequences involving floor and ceiling functions

A closed form expression for the Nth partial sum of the pth powers of ¦vn¦ is obtained, where ¦ · ¦ denotes the nearest integer function. As a consequence, a necessary and sufficient condition for the divisibility of n by ¦vn¦ is derived together with a closed form expression for the least nonnegative residue of n modulo ¦vn¦. In addition an identity involving the zeta function ?(s) and the infinite series ?8(superscript)n=1(subscript) 1/ ||vn|| s+1(superscript) for real s > 1 is also obtained. Formatted abstract is available at http://rmmc.asu.edu/abstracts/rmj/vol36-5/nyblpag1.pdf .