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sympy_divisor_sigma

Compute the divisor function sigma_k(n), returning the sum of the k-th powers of the divisors of n.

Instructions

Divisor function.

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
kYes
nYes

Output Schema

TableJSON Schema
NameRequiredDescriptionDefault
resultYes
Behavior1/5

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

No annotations provided; description fails to disclose behavioral traits such as return values, domain restrictions, or side effects. Being the only text, it is insufficient.

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

Conciseness2/5

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

Extremely terse (two words); under-specification does not serve clarity. Conciseness is not beneficial when it omits essential information.

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

Completeness1/5

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

Despite an output schema, the description provides almost no context about usage, parameters, or behavior, leaving the tool poorly defined for an agent.

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

Parameters1/5

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

Schema parameter names k and n are unexplained. With 0% schema description coverage, the description should clarify them but does not.

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

Purpose2/5

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

Description 'Divisor function' is vague; does not specify which variant (e.g., sum of divisors, number of divisors). It barely adds context beyond the name.

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 guidance on when to use this tool versus alternatives like sympy_divisors or sympy_totient. The description lacks usage context.

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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