divisor_count

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

No annotations are provided, so the description carries full burden. It mentions the mathematical function but doesn't disclose behavioral traits like input constraints (e.g., negative numbers, zero, large integers), performance characteristics, or what happens with invalid inputs. The description is mathematically accurate but operationally incomplete.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Is the description appropriately sized, front-loaded, and free of redundancy?

The description is extremely concise and front-loaded, with a single sentence that directly states the tool's purpose and mathematical context. Every word earns its place, and there's no redundant information.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

Given no annotations, 0% schema coverage, and no output schema, the description is incomplete. It doesn't explain the return value (e.g., integer count), error handling, or practical usage details. For a tool with minimal structured data, the description should provide more operational context.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema description coverage is 0%, so the description must compensate. It explains that parameter 'n' represents 'a number' for which divisors are counted, adding semantic meaning beyond the schema's type declaration. However, it doesn't specify constraints (e.g., positive integers only) or examples, leaving gaps.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Does the description clearly state what the tool does and how it differs from similar tools?

The description clearly states the tool's purpose with a specific verb ('Count') and resource ('positive divisors of a number'), and distinguishes it from siblings by specifying the mathematical function (divisor function τ(n)). It also provides domain and category context, making it highly specific.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Does the description explain when to use this tool, when not to, or what alternatives exist?

The description provides no guidance on when to use this tool versus alternatives. While it mentions the domain (arithmetic) and category (number_theory), it doesn't specify when this tool is appropriate compared to other divisor-related tools like 'divisors' or 'divisor_sum' in the sibling list.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.