▎ 摘　　要

The infinite pairwise summation of the potential energy between an atom above a graphene sheet and carbon atoms arranged in a hexagonal lattice is considered. Its magnitude depends on the minimum distance between the atom and the graphene sheet, as well as the number of carbon atoms on concentric circles, whose center exists under the atom. Using an analytical expression for an upper bound on the number of carbon atoms on a circle, which is the number of solutions to a Diophantine equation, an upperbound on the magnitude of the interaction potential energy between a carbon atom and a graphene sheet is obtained. Upper and lower bounds on the van der Waals interaction potential are calculated as a specific example.