#integers

Generate famous integer sequences and test membership, with exact big-integer maths. The generate endpoint returns the first N terms of a sequence — Fibonacci, Lucas, prime numbers, triangular, square, cube, factorial, Catalan, pentagonal and tetrahedral numbers, plus parameterised arithmetic (a start and a step), geometric (a start and a ratio) and powers (any base). The contains endpoint tells you whether a given number belongs to a sequence — is 233 a Fibonacci number, is 21 triangular, is 97 prime, is 720 a factorial — using fast closed-form tests for primes, squares, cubes, triangular, pentagonal and Fibonacci numbers and an exact search for the rest, and it returns the term index where it is known. Because everything is computed with arbitrary-precision integers, terms beyond the usual floating-point limit are returned exactly as decimal strings and never overflow. It runs entirely locally, so it is instant, deterministic and private. Ideal for education and maths tooling, coding challenges and puzzles, test-data generation, recreational mathematics and number-theory experiments. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This generates and tests integer sequences; to factorize a single number or get its divisors use a number-theory API.

api.oanor.com/sequences-api

An integer toolkit as an API. Factorize any number into its prime factors with exponents (and a readable 2^3 × 3^2 × 5 form), with the divisor count, the divisor sum, the full list of divisors and whether the number is perfect; find the greatest common divisor and least common multiple of two numbers (and whether they are coprime); and test primality, returning the next and previous prime. Handles numbers up to a trillion. Perfect for maths education and puzzles, cryptography demos, generating test data and any time you need the building blocks of a number. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 4 endpoints. A focused integer toolkit, distinct from a general math-expression engine.

api.oanor.com/numbertheory-api