A260823 Positive integers that are not divisible by any cube greater than 1 and cannot be written as the sum of two cubes of rational numbers.

3, 4, 5, 10, 11, 14, 18, 21, 23, 25, 29, 36, 38, 39, 41, 44, 45, 46, 47, 52, 55, 57, 59, 60, 66, 73, 74, 76, 77, 82, 83, 93, 95, 99, 100, 101, 102, 109, 111, 113, 116, 118, 119, 121, 122, 129, 131, 137, 138, 145, 146, 147, 148, 149, 150, 154, 155, 158, 165

Offset

1,1

Comments

This sequence is infinite.

This sequence is the complement of (A020897 minus A046099), except 1.

References

W. Sierpiński, 250 Problems in Elementary Number Theory, 1970, page 112.

Links

Table of n, a(n) for n=1..59.

Steven R. Finch, On a Generalized Fermat-Wiles Equation [broken link]

Steven R. Finch, On a Generalized Fermat-Wiles Equation [From the Wayback Machine]

Ernst S. Selmer, The diophantine equation ax^3 + by^3 + cz^3 = 0, Acta Math. 85 (1951), pp. 203-362.

Example

a(4)=10 cannot be written as c^3 + d^3 where both c and d are rational numbers.
22 = (25469/9954)^3 + (17299/9954)^3, so 22 is not in the sequence.

Crossrefs

Cf. A003325, A020897, A046099.

Sequence in context: A274519 A139445 A185345 * A359486 A135114 A240789

Adjacent sequences: A260820 A260821 A260822 * A260824 A260825 A260826

Keyword

nonn,more

Author

Marco Ripà, Jul 31 2015

Status

approved