ScorpTech x402 Tools

Sigma K

sigma_k

Read-onlyIdempotent

The sum of the kth powers of the divisors of n. sigma_2(1) is 1, sigma_2(6) is 50, and sigma_2(12) is 210. n runs from 1 to 1000000000000, and k runs from 2 to 12. Past 15 digits the value 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/sigma-k

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>",
      "k": "<k>"
    },
    "name": "sigma_k"
  }
}

Input Schema

Name	Required	Description	Default
`k`	Yes
`n`	Yes

Schema Changelog

Changes observed during successful MCP inspections.

AddedOct 23, 2026

TDQS

A3.8/5.0

Behavior4/5

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

Annotations already declare read-only, idempotent, non-destructive and open-world behavior, so the safety profile is covered. The description adds genuinely new behavioral facts: the response becomes a decimal string past 15 digits, pricing is $0.001 USDC per successful call via x402 on Solana, and an equivalent HTTPS endpoint exists.

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 definition is front-loaded, followed by concrete examples, bounds, output-format caveat, and payment/endpoint details. Each sentence serves a purpose, though the three examples could arguably be trimmed to one without losing much.

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?

With no output schema, the description does explain the return type boundary (decimal string past 15 digits). Combined with the domain bounds, pricing model and alternate endpoint, an agent has everything needed to call it, assuming sub-15-digit results are numeric as implied.

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

Parameters4/5

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

Schema coverage is 0%, so the description carries the full burden of explaining the parameters. It defines what n and k mean (divisors of n, kth powers) and restates their ranges, and the worked examples pin down the exact semantics of k – far more than the bare minimum/maximum in the 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 gives a precise mathematical definition ('sum of the kth powers of the divisors of n') plus worked examples, which makes the computation unambiguous. It's clear enough that an agent can distinguish it from the sibling divisor_sum (the k=1 case), though it never names that sibling explicitly.

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?

Usage is only implied by the domain of n and k and the examples; there is no explicit 'use this when…' or comparison against alternatives like divisor_sum or unitary_sigma. The example inputs do help an agent confirm its interpretation before calling.

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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