Erdős problem 940

Let $r \ge 3$ . Is it true that the set of integers which are the sum of at most $r$ $r$ -powerful numbers has density $0$ ?

Sources

The source's own material, retained exactly.

5 retained statements36c6d0fef71a

FormalConjectures/ErdosProblems/

940.lean

Retained formal statement4 of 5

Heath-Brown [He88] has proved that all large numbers are the sum of at most three $2$ -powerful numbers.

[He88] Heath-Brown, D. R., Ternary quadratic forms and sums of three square-full numbers. (1988), 137--163.

FormalConjectures/ErdosProblems/940.leanErdos940.erdos_940.variants.three_powerful1 lineExact file

1∀ᶠ (x : ℕ) in Filter.atTop, ∃ S, S.card ≤ 3 ∧ (∀ s ∈ S, Nat.Full 2 s) ∧ x = S.sum

SolvedStatement only, no proof