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

Beyond the readOnly/idempotent annotations, it discloses the notable behavior that non-integer results are rejected rather than rounded, plus the cost ($0.001 USDC per successful call, x402/Solana) and an alternate HTTPS endpoint. That is real operational context the annotations do not carry; only the exact error shape is left unspecified.

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 core definition and examples come first, followed by the rejection rule, domain, and pricing/endpoint details, so it is well front-loaded. The pricing and alternate-endpoint sentences are operational rather than computational but plausibly earn their place for an agent deciding whether to call.

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 one-parameter, no-output-schema tool the description supplies the definition, the input domain, the failure condition, and demonstrated return values via examples, which is essentially everything needed to call it correctly. Only a formal statement of the return type/error payload is absent.

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 carry the meaning of 'n'; it does, by framing n as the integer whose divisors are averaged and restating the 1..1000000 domain. The worked examples further clarify which values are accepted, so the single undocumented parameter is effectively covered.

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 gives a precise mathematical definition (the average of the divisors of n) plus six worked examples that pin down the computation exactly. It does not name or contrast any sibling (e.g. arithmetic_number, abundancy, arithmetic_count), so an agent still has to infer the boundary against the many related tools in this family.

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?

It states the valid input domain (n from 1 to 1000000) and that a non-integer average is rejected, which tells the agent when the call will fail. There is no explicit guidance about when to prefer this over the neighbouring arithmetic/divisor tools, so the usage guidance is implied rather than stated.

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