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Number Theory Calculator

A full number-theoretic profile of any integer from 1 to 1,000,000 : primality, prime factorization, Euler totient φ(n) , divisors, perfect / abundant / deficient class, Liouville λ, Möbius μ and the Collatz trajectory.

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Prime factorization
28 =2²×7
Ω(n) = 3 with multiplicity · ω(n) = 2 distinct
Primality
composite
Euler totient φ(n)
12
coprime to n below n
Divisors d(n)
6
including 1 and n
Sum of divisors σ(n)
56
Classification
perfect
proper divisors sum to 28
Liouville λ(n)
−1
(−1)^Ω(n), Ω = 3
Möbius μ(n)
0
has a squared prime factor
Digit sum
10
digital root 1
Properties
Perfect squareno
no integer square root
Perfect cubeno
no integer cube root
Carmichaelno
fails Korselt’s criterion
Divisors6 total · primes highlighted
12471428
Collatz trajectory19 steps to reach 1 · peak 52
even → n/2 odd → 3n+1
28 → 14 → 7 → 22 → 11 → 34 → 17 → 52 → 26 → 13 → 40 → 20 → 10 → 5 → 16 → 8 → 4 → 2 → 1
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