On positive integers with a certain nondivisibility property.
We use the properties of -adic integrals and measures to obtain general congruences for Genocchi numbers and polynomials and tangent coefficients. These congruences are analogues of the usual Kummer congruences for Bernoulli numbers, generalize known congruences for Genocchi numbers, and provide new congruences systems for Genocchi polynomials and tangent coefficients.
In this paper it is discus a relation between -density and -density. A generalization of Šalát’s result concerning this relation in the case of asymptotic density is proved.