"The" Smarandache constant is the smallest solution to the generalized Andrica's conjecture, x≈0.567148 (OEIS A038458). The first Smarandache constant is defined as S_1 congruent sum_(n = 2)^∞ 1/([μ(n)]!) = 1.09317... (OEIS A048799), where μ(n) is the Smarandache function. Cojocaru and Cojocaru (1996a) prove that S_1 exists and is bounded by 0.717

Andrica's conjecture | Smarandache function