Ramanujan number

1729

               1729 is the natural number following 1728 and preceding 1730. 1729 is known as the Hardy- Ramanujan number after a famous anecdote of the British mathematician G.H. Hardy regarding a visit to the hospital to see the Indian mathematician Srinivasa Ramanujan. As told by Hardy; " I remember once going to see him ( Ramanujan) when he was lying ill at Putney. i had ridden in taxi cab No. 1729, and remarked that the number seemed to be rather a dull one, and that i hoped it was not an favorable omen. "NO", he replied, "it is a very interesting number, it is the smallest number expressible as the sum of two [positive] cubes in two different ways." the number was also found in one of Ramanujan's notebooks dated years before the incident.

some of the properties of 1729:

1. it can be represent as a product of 3 distinct prime numbers.

2. 1729 is divisible by sum of its digits. Hence its a Harshad number. 1729/19=91

3. 1729 is the smallest number expressible as the sum of two positive cubes in two different ways. the different ways are ;1729 = 1³ + 12³ = 9³ + 10³.

4.1729 is the third Carmichael number and the first absolute Euler pseudo prime.

5. 1729 is a Zeisel number. it is a centered cube number, as well as a dodecagonal number.

6. 1729 is one of four positive integer which, when its digits are added together, produces a sum which, when multiplied by its reversal, yields the original number.
     1+ 7 + 2 + 9 = 19
      19 x 91 =1729