A391767 Least positive integer k, such that the equation x^3 + 2*y^3 = k has exactly n sets of different integer solutions (x, y) where GCD(x, y) = 1.

3, 1, 62, 899, 50466457

Offset

1,1

Links

Table of n, a(n) for n=1..5.

Fang, How to find the least integer n such that the equation x^3+2y^3=n has at least 6 distinct solutions, where GCD(x,y)=1?

Example

a(1) = 3 since 3 = 1^3 + 2*1^3.
a(2) = 1 since 1 = 1^3 + 2*0^3 = (-1)^3 + 2*1^3.
a(3) = 62 since 62 = (-34)^3 + 2*27^3 = 2^3 + 2*3^3 = 4^3 + 2*(-1)^3.
a(4) = 899 since 899 = (-223)^3 + 2*177^3 = (-5)^3 + 2*8^3 = 11^3 + 2*6^3 = 43^3 + 2*(-34)^3.
a(5) = 50466457 since 50466457 = (-269)^3 + 2*327^3 = (-71)^3 + 2*294^3 = 415^3 + 2*(-219)^3 = 739^3 + 2*(-561)^3 = 24697^3 + 2*(-19602)^3.

Crossrefs

Cf. A093193, A219726, A219728.

Sequence in context: A189898 A082525 A162221 * A213127 A361091 A344050

Adjacent sequences: A391764 A391765 A391766 * A391768 A391769 A391770

Keyword

nonn,more

Author

Zhining Yang, Dec 19 2025

Status

approved