Let ø denote Euler's phi function. For a fixed odd prime q we investigate the first and second order terms of the asymptotic series expansion for the number of n ⩽ x such that q ∤ ø (n). Part of the ...

The most important example of such operators is the Euler operator 𝐸 (from the variational calculus) being the one in question depending only on Lagrangians. We describe all formal Euler like ...