Deficient Numbers: Returns deficient numbers up to a limit, where the sum of proper divisors is less than the number 🆓 5 free trial calls per signed wallet
This tool declares no required parameters. Add optional parameters from the input schema as needed.
{
"id": 1,
"jsonrpc": "2.0",
"method": "tools/call",
"params": {
"arguments": {},
"name": "x402-deficient-numbers"
}
}| Name | Required | Description | Default |
|---|---|---|---|
| n | No | ||
| limit | No |
Changes observed during successful MCP inspections.
Input schema / properties / limit / descriptionRemoved value: -"Limit to process"Input schema / properties / n / descriptionRemoved value: -"N to process"Input schema / properties / limitAdded value: +{
+ "description": "Limit to process",
+ "type": "string"
+}Input schema / properties / nAdded value: +{
+ "description": "N to process",
+ "type": "string"
+}Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the burden. It usefully discloses the monetization model (5 free trial calls per signed wallet), which is genuine behavioral context. But it says nothing about output format, ordering, bounds on limit, or what happens on invalid input.
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?
Front-loads the purpose in a single readable sentence, but the trailing emoji promo about free trial calls is marketing noise that dilutes the definition, and the two distinct ideas (what it computes, billing) are run together.
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?
With no annotations, no output schema, and 0% schema description coverage across two parameters (one entirely unexplained), the description does not supply enough for an agent to call this correctly, e.g. it never explains `n` or the accepted form of `limit`.
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 coverage is 0% and neither parameter is documented. The phrase 'up to a limit' loosely maps to the `limit` parameter, but the `n` parameter is never mentioned or explained at all, leaving half the inputs opaque in both schema and description.
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?
States a specific result (list of deficient numbers up to a limit) and even defines the mathematical predicate, so an agent knows what it computes. However, it never distinguishes itself from close siblings such as x402-abundant-numbers, x402-perfect-numbers, or x402-is-deficient-number, which an agent must choose between.
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?
There is no guidance on when to use this tool versus x402-is-deficient (single-number test) or the other divisor-class list tools. The only contextual note is the free-trial/payment line, which is billing information, not usage routing.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
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