Computational investigation of Lehmer's Totient Problem

Abstract. Let \(N\) a composite number for which \(k\cdot\varphi(N)=N-1\). We can state that if \(3 \mid N\) then \(\omega(N) \geq 40 \ 000 \ 000 \mbox{ and } n > 10^{360 \ 000 \ 000}\).