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IBM

MCP Math Server

by IBM

aliquot_sequence_analysis

Analyze aliquot sequences to compute successive sums of proper divisors from a starting integer, identifying patterns and termination points in mathematical sequences.

Instructions

Analyze aliquot sequence starting from n. (Domain: arithmetic, Category: special_numbers)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
nYes
max_stepsNo
Behavior2/5

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

No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions 'Analyze aliquot sequence' but doesn't specify what the analysis returns (e.g., sequence terms, cycle detection, length), whether it has computational limits, or error handling. This leaves significant gaps in understanding the tool's behavior for an AI agent.

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 concise with a single sentence and parenthetical tags, making it easy to parse. However, it could be more front-loaded by specifying the output or key behaviors upfront to improve utility for an AI agent.

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

Completeness2/5

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

Given no annotations, 0% schema description coverage, and no output schema, the description is incomplete. It lacks details on return values, error conditions, performance characteristics, and how parameters affect the analysis, making it insufficient for a tool with mathematical complexity.

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

Parameters2/5

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

Schema description coverage is 0%, so the description must compensate for undocumented parameters. It mentions 'starting from n' which clarifies the 'n' parameter, but doesn't explain 'max_steps' (e.g., its purpose as a limit on iterations, default behavior, or implications). With two parameters and no schema descriptions, this is inadequate.

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

Purpose3/5

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

The description states the tool 'Analyze aliquot sequence starting from n' which provides a clear verb ('Analyze') and resource ('aliquot sequence'), but it's somewhat vague about what 'analyze' entails (e.g., compute terms, detect cycles, etc.). It distinguishes from siblings by specifying 'aliquot sequence' (a mathematical concept), but doesn't explicitly differentiate from similar tools like 'collatz_sequence' or 'digital_sum_sequence' beyond the domain/category tags.

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

Usage Guidelines2/5

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

No explicit guidance on when to use this tool versus alternatives is provided. The description includes domain and category tags ('Domain: arithmetic, Category: special_numbers'), which imply a mathematical context, but there's no mention of prerequisites, when-not-to-use scenarios, or comparisons to sibling tools like 'collatz_sequence' or 'digital_sum_sequence' that also analyze sequences.

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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