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

Author

Marco Ripà, Jul 31 2015

Keywords

• nonn
• more

Comments

This sequence is infinite.

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

Examples

			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.
		

References

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

Links

• 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.

Crossrefs

Cf. A003325, A020897, A046099.