Number Gossip
(Enter a number and I'll tell you everything you wanted to know about it but were afraid to ask.)
Unique Properties of 1729
- 1729 is a Ramanujan number, also called a taxi-cab number, the smallest number representable in two ways as a sum of two cubes: 1729 = 13+123 = 93+103
- 1729 is the smallest number that is a pseudoprime simultaneously to bases 2, 3 and 5
- Web pages about 1729:
- 1729 is the smallest Carmichael number n such that n-1 is a perfect power
- 1729 is the smallest Carmichael number whose prime factors form an arithmetic progression
- 1729 is the largest number which, when its digits are added together, produces a sum which, when multiplied by its reversed self, yields the original number
- 1729 is the product of the first three happy primes
- 1729 is the smallest Carmichael number such that its Euler totient function is a perfect square
- 1729 is the smallest phi-radical number: composite number n such that rad(φ(n)) = rad(n-1)