Erdős 1054: sums of smallest divisors
A complete Lean 4 proof of all three parts of Erdős problem 1054. For the least integer f(n) whose k smallest divisors sum to n, we prove that f(n) is not o(n), is not o(n) on any density-one set, and satisfies limsup f(n)/n = ∞ on every density-one subtype. Building on the qualitative divisor-prefix sieve and almost-all binary Goldbach proof from Principia-Math-Solutions, this formalization proves the Formal Conjectures statements along with a sharp second-moment lower-density bound c / [A^3 (1 + log A)^4] for odd n with f(n) > A n, the Tao–Kovač small-ratio upper bound #{n ≤ X : 0 0}…
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