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Divisor Sum

divisor_sum
Read-onlyIdempotent

The sum of the positive divisors of n. sigma(6) is 12 and sigma(28) is 56. n = 0 is rejected. A value past 15 digits is a decimal string. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/divisor-sum

Tool call template

Replace each placeholder with a value matching the input schema. Only required parameters are included; add optional parameters as needed.

{
  "id": 1,
  "jsonrpc": "2.0",
  "method": "tools/call",
  "params": {
    "arguments": {
      "n": "<n>"
    },
    "name": "divisor_sum"
  }
}

Input Schema

NameRequiredDescriptionDefault
nYes

Schema Changelog

Changes observed during successful MCP inspections.

  1. Added

TDQS

A3.7/5.0
Behavior4/5

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

Annotations already declare readOnlyHint, idempotentHint, openWorldHint, and destructiveHint=false, so the safety profile is clear. The description adds useful behavioral context: the $0.001 USDC x402 payment cost, the Solana payment context, and an HTTPS alternative endpoint, which are not present in the annotations.

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

Conciseness4/5

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

The description is front-loaded with the core definition and examples, followed by constraints and pricing details. It is compact and each sentence generally serves a purpose, though the pricing and endpoint information could be seen as ancillary to the mathematical purpose.

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

Completeness4/5

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

For a simple one-parameter mathematical tool with no output schema, the description is largely complete: it defines the operation, gives examples, states an edge case, and provides access/pricing context. Minor ambiguity around the decimal-string note versus the integer schema prevents a perfect score.

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

Parameters3/5

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

With only one parameter and 0% schema description coverage, the description must compensate. It adds that n = 0 is rejected and that values beyond 15 digits are expressed as a decimal string, which is useful, but the schema already defines n as an integer with a maximum of 1e12, making the 'past 15 digits' note only partially relevant and slightly inconsistent with the declared schema.

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

Purpose4/5

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

The description states a specific mathematical operation: the sum of positive divisors of an integer n, and gives examples sigma(6)=12 and sigma(28)=56. This clearly separates it from a generic arithmetic tool, but it does not explicitly distinguish it from related siblings such as divisor_count, sigma_k, or aliquot.

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

Usage Guidelines3/5

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

It provides edge-case guidance (n = 0 is rejected, values past 15 digits are passed as a decimal string), which implies when the tool is valid. However, it does not state when to use this tool versus alternatives like divisor_count or sigma_k, and no explicit when-not guidance beyond n = 0.

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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