OFFSET
1,2
COMMENTS
The table in Alaca & Williams (2004) skips over n = 4, 9, 16 but includes 12, 18 and 20; then there is a footnote to the table explaining that Q(4^(1/3)) and Q(16^(1/3)) work out to be subdomains of Q(2^(1/3)), and similarly for Q(9^(1/3)) and Q(3^(1/3)) and for Q(18^(1/3)) and Q(12^(1/3)).
REFERENCES
Şaban Alaca & Kenneth S. Williams, Introductory Algebraic Number Theory. Cambridge: Cambridge University Press (2004): 176-177, Theorem 7.3.2 on the former page, Table 1 on the latter page.
FORMULA
EXAMPLE
a(7) = -1323 because the seventh cubefree number is 7 and Q(7^(1/3)) has -1323 for a discriminant.
a(8) = -243 because the eighth cubefree number is 9 and Q(9^(1/3)) is a subdomain of Q(3^(1/3)), which has a discriminant of -243.
MATHEMATICA
DeleteCases[Table[Boole[FreeQ[FactorInteger[n], {_, k_ /; k > 2}]] * NumberFieldDiscriminant[n^(1/3)], {n, 100}], 0]
CROSSREFS
KEYWORD
sign
AUTHOR
Alonso del Arte, May 24 2014
STATUS
approved