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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.
0
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
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
KEYWORD
nonn,more
AUTHOR
Marco Ripà, Jul 31 2015
STATUS
approved