divisor_power_sum

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

No annotations are provided, so the description carries full burden. It states what the tool calculates but doesn't disclose behavioral traits: no information about input constraints (e.g., valid ranges for n and k), performance characteristics, error handling, or output format. The description is purely functional without operational context.

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 - a single sentence with mathematical notation and domain tags. Every element earns its place: the mathematical definition is essential, and the domain/category provides helpful classification. No wasted words or 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?

For a mathematical function tool with 2 parameters, 0% schema coverage, no annotations, and no output schema, the description is inadequate. It doesn't explain parameter meanings, constraints, return values, or how this differs from related divisor functions. The mathematical notation alone is insufficient for an AI agent to use the tool correctly without additional 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 schema provides no parameter documentation. The description mentions 'n' and 'k' in the mathematical notation σ_k(n) but doesn't explain what these parameters represent (n=integer whose divisors are considered, k=exponent applied to each divisor). It provides minimal semantic context beyond the mathematical formula.

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: 'Calculate σ_k(n) - sum of kth powers of divisors.' It specifies the mathematical function and includes domain/category context. However, it doesn't explicitly differentiate from sibling tools like 'divisor_sum' or 'divisor_count' that handle related divisor functions.

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 the domain/category tags ('arithmetic', 'arithmetic_functions') give broad context, there's no explicit comparison to sibling tools like 'divisor_sum' (which appears to be the k=1 case) or 'divisor_count' (k=0 case), nor any prerequisites or typical use cases.

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