There are equivalent formulations of the Riemann hypothesis (RH) by G. Robin (1984, using Euler-constant ) and J. C. Lagarias [Am. Math. Mon. 109, No. 6, 534–543 (2002; Zbl 1098.11005), using harmonic numbers). The authors give another elementary one, using Gronwall’s function : RH is true if and only if is the only composite number with the two properties:
(i) for every prime factor of ;
(ii) for every positive integer .
The proof is elementary and uses the results of Gronwall and Robin.