Num Analyzer

Mathematical Principles & Theorems

Analyzes integer properties in arithmetic and analytic number theory: Primality (no divisors other than 1 and \(n\)), Perfect numbers (\(\sigma(n) - n = n\), e.g., 6, 28, 496 linked to Mersenne primes via Euclid-Euler theorem \(2^{p-1}(2^p-1)\)), Abundant (\(\sigma(n) > 2n\)) and Deficient numbers, Armstrong / Narcissistic numbers (\(\sum d_i^k = n\)), Harshad numbers (\(n \equiv 0 \pmod{\sum d_i}\)), and Automorphic numbers (\(n^2\) terminates in \(n\)).

Operating Instructions

• Enter any positive integer \(n\) in the numeric input box.
• Click Analyze to compute prime factors, total divisor count \(d(n)\), and sum of divisors \(\sigma(n)\).
• Review the verified mathematical classification badges (Prime, Perfect, Armstrong, Harshad, etc.).
• Examine the divisor lattice and prime power factor expansion.