Number Properties Explorer
Enter a non-negative integer and see its classification across two dozen number-theoretic properties at once — primality, the aliquot class (perfect / abundant / deficient), happy, narcissistic (Armstrong), Kaprekar, Smith, automorphic, and membership in the triangular, square, pentagonal, Fibonacci, Catalan, and factorial sequences — plus its divisor structure, prime factorization, digit sum, and digital root. Everything runs locally in your browser.
Properties
A perfect number equals the sum of its proper divisors (6 = 1+2+3); abundant if that sum exceeds it, deficient if below. A happy number reaches 1 by iterating the sum of squared digits; otherwise it falls into the 4 → 16 → 37 → … cycle. A narcissistic (Armstrong) number equals the sum of its digits each raised to the count of digits (153 = 1³+5³+3³). A Kaprekar number n has n² splittable into left + right (right > 0) that sums to n (9² = 81, 8+1 = 9). A Smith number is composite with digit sum equal to the digit sum of its prime factorization. An automorphic number's square ends in itself (76² = 5776). Triangular/square/pentagonal/Fibonacci/Catalan/factorial test membership in those sequences. Harshad (Niven) numbers are divisible by their digit sum; the digital root is the single digit obtained by repeated digit-summing. Pairs with the Prime Explorer, Prime Factorization, and Divisors tools. Runs locally — nothing leaves your browser.