The OEIS is supported by the many generous donors to the OEIS Foundation. Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 60th year, we have over 367,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 Table of n, a(n) for n=1..41. 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 8 04:48 EST 2023. Contains 367662 sequences. (Running on oeis4.)