practical_six
plain-language theorem explainer
The declaration confirms that the sum-of-divisors function satisfies σ_1(6) ≥ 6, establishing 6 as practical. Number theorists working with divisor sums or practical numbers would cite this verification. The proof executes as a one-line native decision procedure that evaluates the concrete inequality directly.
Claim. The sum-of-divisors function satisfies $σ_1(6) ≥ 6$.
background
The module supplies lightweight wrappers around Mathlib's arithmetic function library, beginning with the Möbius function μ and extending to the sum-of-divisors function σ_k. The sigma abbreviation is defined as ArithmeticFunction.sigma k, the standard sum-of-divisors function. The local setting keeps statements lightweight pending deeper Dirichlet algebra and inversion.
proof idea
The proof is a one-line wrapper that applies native_decide to evaluate the concrete inequality σ_1(6) ≥ 6.
why it matters
This verification supplies a concrete instance in the NumberTheory.Primes.ArithmeticFunctions module. It instantiates the practical-number condition noted in the declaration comment. No downstream uses appear in the used-by graph.
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