1729

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Summary

Names

This number is called the Hardy-Ramanujan number after a conversation between Hardy and Ramanujan where Ramanujan observed that it is the smallest number expressible as the sum of two cubes in two distinct ways: $\!1729=10^{3}+9^{2}3=12^{3}+1^{3}$.

Factorization

$\!1729=7\cdot 13\cdot 19$

Properties and families

Property or family	Parameter values	First few numbers
Carmichael number	third among them	561, 1105, 1729, ...
Poulet number (Fermat pseudoprime to base 2)	sixth among them	341, 561, 645, 1105, 1387, 1729, 1905, 2047