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 A242867 Discriminants of cubic domains for cubefree n. 1
 1, -108, -243, -108, -675, -972, -1323, -243, -300, -3267, -972, -4563, -5292, -6075, -867, -972, -1083, -2700, -11907, -13068, -14283, -675, -2028, -588, -22707, -24300, -25947, -29403, -31212, -3675, -972, -4107, -38988, -41067, -45387, -47628, -49923, -1452, -6075, -6348, -59643 (list; graph; refs; listen; history; text; internal format)
 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. LINKS FORMULA Set m = A004709(n), then express it as m = h * k^2, where k = A000188(m), the square root of the largest square dividing m, and h = m/k^2 = A007913(m). Then: a(n) = -3h^2 * k^2 if m == +-1 (mod 9), otherwise a(n) = -27h^2 * k^2. This formula is from Theorem 7.3.2 in Alaca & Williams (2004). 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 Cf. A004709 (cubefree numbers). Sequence in context: A235292 A202202 A202195 * A255091 A255084 A252337 Adjacent sequences:  A242864 A242865 A242866 * A242868 A242869 A242870 KEYWORD sign AUTHOR Alonso del Arte, May 24 2014 STATUS approved

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Last modified September 23 19:28 EDT 2020. Contains 337315 sequences. (Running on oeis4.)