six_almost_prime_fivehundredfortyfour
plain-language theorem explainer
The theorem confirms that 544 factors as 2^5 times 17 and therefore carries exactly six prime factors counted with multiplicity. Researchers extending arithmetic functions for Recognition Science reference this instance because the prime 17 is flagged as relevant. The proof reduces the claim to a direct computational check of the total prime factor count.
Claim. $Ω(544)=6$, where $Ω(n)$ counts the prime factors of $n$ with multiplicity and $544=2^5×17$.
background
The module supplies lightweight wrappers around Mathlib arithmetic functions, beginning with the Möbius function as a foothold for later inversion work. A natural number is six-almost-prime when the total number of prime factors counted with multiplicity equals six; the predicate implements this by returning true exactly when that count holds. The local setting keeps statements minimal so that Dirichlet algebra can be added once the basic interfaces stabilize.
proof idea
The proof is a one-line term that invokes native_decide to evaluate the predicate directly from the definition that reduces to the total prime factor count equaling six.
why it matters
This supplies a concrete six-almost-prime example involving the RS-relevant prime 17 inside the arithmetic functions layer. It supports the Möbius footholds described in the module documentation and sits among sibling results on squarefree checks and bigOmega. No downstream theorems depend on it yet, so its role remains as a verified data point for future number-theoretic constructions in the framework.
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