Sphenic number: n = p·q·r for three distinct primes. Smallest: 30=2·3·5, 42=2·3·7, 66=2·3·11, 70=2·5·7, 78=2·3·13... Always has exactly 8 divisors: 1,p,q,r,pq,pr,qr,pqr. μ(n)=−1 (Möbius function). About 30% of numbers up to 1000 are sphenic.
How to Use
Enter n:
- Sphenic?: Product of 3 distinct primes?
- Factors: The three primes
- Divisors: All 8 divisors
Properties
- Exactly 8 divisors
- μ(n) = −1 (squarefree with odd # of prime factors)
- φ(n) = (p−1)(q−1)(r−1)
- σ(n) = (1+p)(1+q)(1+r)
Density
Sphenic numbers have positive density! About 30% of integers ≤1000 are sphenic. The density can be computed from the prime number theorem. They're much more common than primes for large N.
Step-by-Step Instructions
- 1Enter number.
- 2Check sphenic.
- 3View three primes.
- 4List all 8 divisors.
- 5Browse sequence.