PROVED (LEAN), the site's label. The status-defining source is Haight's theorem (Mathematika 26 (1979), 53--61, refereed): for every $c$ some $n$ has $\sigma(n)>cn$ while its divisors above $1$ cannot be the moduli of a covering system, so the answer is yes; the claim page is Haight (accepted on the refereed publication and the site's credit). A second, quantitative proof by Filaseta, Ford, Konyagin, Pomerance and Yu (J. Amer. Math. Soc. 2007, refereed) is recorded on their claim page (Filaseta, Ford, Konyagin, Pomerance and Yu, 2005). The site's Lean qualification refers to the Lean proof recorded under Formalization.