AlmostPerfectNumbers.lean`

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Project sources: Pinned project documentation, Formal Conjectures paper, arXiv v1

2 declarations, 1 contain sorry, 0 declared as axioms

Non-Power-of-2 Almost Perfect Numbers Conjecture

References:

Imports (1)

FormalConjecturesUtil

def AlmostPerfectNumbers.AlmostPerfect A number is almost perfect if the sum of its divisors is equal to $2n - 1$ line 40 source
Source documentation
A number is almost perfect if the sum of its divisors is equal to $2n - 1$.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Nat
Proof uses: Eq, HAdd.hAdd, OfNat.ofNat, ArithmeticFunction, ArithmeticFunction.sigma, HMul.hMul
9 instances, coercions and auxiliary constants left out.
```
def AlmostPerfect (n : ℕ) : Prop :=
…
```
theorem AlmostPerfectNumbers.exists_almost_perfect_not_power_of_two Non-Power-of-2 Almost Perfect Numbers Conjecture sorry line 48 source
Source documentation
Non-Power-of-2 Almost Perfect Numbers Conjecture. Does there exist an almost perfect number that is not a power of 2?

depends on sorry what this means
Statement uses: Iff, True, Exists, Nat, And, AlmostPerfectNumbers.AlmostPerfect, Not, Eq, HPow.hPow, OfNat.ofNat
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
10 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem exists_almost_perfect_not_power_of_two :
    answer(sorry) ↔ ∃ n : ℕ, AlmostPerfect n ∧ ¬ ∃ k : ℕ, n = 2^k := by
…
```
Mentions: AlmostPerfectNumbers.AlmostPerfect