numclassify

Given a number, what is it?

Most number-theory libraries -- labmath, eulerlib, pyntlib -- compute things: factor integers, find GCDs, generate primes. numclassify solves a different problem. Hand it an integer and it tells you every named mathematical type that number belongs to, across 2140+ categories, with zero external dependencies.

153   →  Armstrong, Harshad, Triangular, Deficient, ...
1729  →  Taxicab (Hardy–Ramanujan), Carmichael, Harshad, ...
28    →  Perfect, Triangular, Hexagonal, Harmonic Divisor, ...

Try it live: numclassify Playground

---

Installation

pip install numclassify

Python 3.8 - 3.13. No external dependencies.

---

Quick example

import numclassify as nc

nc.classify(1729)
# {
#   'number': 1729,
#   'score': 25,
#   'notable_score': 19,
#   'true_properties': ['Taxicab', 'Carmichael', ...],
#   'categories': {'primes': [...], 'sequences': [...], ...}
# }

nc.is_prime(17)           # True
nc.is_perfect(28)         # True
nc.get_true_properties(6) # {'Perfect': True, 'Triangular': True, 'Pronic': True, ...}

nc.why("armstrong", 153)
# "153 is Armstrong because: 1^3 + 5^3 + 3^3 = 1 + 125 + 27 = 153"

nc.property_info("armstrong")
# {'name': 'Armstrong', 'category': 'digital', 'oeis': 'A005188', 'examples': [...]}

nc.find(1, 1000, has=["harshad", "palindrome"])

---

Categories

Category	Count
Polygonal figurate	~1003
Centered polygonal	~998
Prime families	41
Digital invariants	13
Divisor-based	27
Sequences	16
Powers	13
Combinatorial	10
Recreational	6
Total	2141

---

Add your own types

from numclassify import register

@register(name="My Type", category="recreational")
def is_my_type(n: int) -> bool:
    return n > 0 and n % 7 == 0

import numclassify as nc
nc.is_my_type(42)  # True — available everywhere immediately

See API Reference for the full function list, or the CLI Reference for command-line usage.