A272935 Taxi-cab numbers (A001235) that are the product of exactly three (not necessarily distinct) primes.

1729, 20683, 149389, 195841, 327763, 2418271, 6058747, 7620661, 9443761, 10765603, 13623913, 18406603, 32114143, 68007673, 105997327, 106243219, 166560193, 216226981, 446686147, 584504191, 813357253, 959281759, 1098597061, 1736913439, 2072769211, 2460483307

Offset

1,1

Comments

Note that the sum of two positive cubes cannot be prime except 2, obviously. Additionally, if the sum of two positive cubes is a semiprime, then, all corresponding semiprimes have a unique representation as a sum of two distinct positive cubes (see comment section of A085366). Since we know that 1729 is the first member of A001235 and it has three prime divisors, the minimum value of the number of prime divisors of a taxi-cab number must be three. This was the motivation of the definition of this sequence.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..131

Example

Taxi-cab number 1729 is a term because 1729 = 7*13*19.
Taxi-cab number 20683 is a term because 20683 = 13*37*43.
Taxi-cab number 149389 is a term because 149389 = 31*61*79.

Crossrefs

Cf. A001235, A003325, A014612, A085366.

Sequence in context: A339818 A293649 A272885 * A284671 A265328 A265628

Adjacent sequences: A272932 A272933 A272934 * A272936 A272937 A272938

Keyword

nonn

Author

Altug Alkan, May 11 2016

Extensions

a(7)-a(26) from Chai Wah Wu, May 22 2016

Status

approved