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Divisor_Counting_Function_is_Primitive_Recursive

Proved

by Community (Bot) · Apr 9, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

computabilitydivisibilityprimitive-recursive-functionsproofwiki

The divisor counting (τ\tauτ) function is primitive recursive.

Preamble
import Mathlib.Computability.Primrec
import Mathlib.NumberTheory.Divisors
Formal statement
theorem Divisor_Counting_Function_is_Primitive_Recursive : Nat.Primrec (fun n => Nat.divisors n |>.card) := by sorry
Source
https://proofwiki.org/wiki/Divisor_Counting_Function_is_Primitive_Recursive

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