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A246457 Given m the n-th cubefree number, A004709(n); a(n) is the class number of field Q(m^(1/3)). 0
1, 1, 1, 1, 1, 3, 1, 1, 2, 1, 3, 3, 2, 1, 1, 3, 3, 3, 3, 1, 1, 3, 3, 1, 3, 3, 1, 3, 3, 1, 3, 3, 6, 1, 3, 12, 1, 1, 1, 2, 3, 1, 3, 3, 1, 1, 6, 6, 1, 3, 6, 3, 6, 18, 6, 6, 3, 1, 9, 1, 3, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,6
COMMENTS
The smallest m for which Q(m^(1/3)) not a unique factorization domain is m = 6, for which the corresponding field has class number 3.
The table in Alaca & Williams includes 63 but excludes 18 and other cubefree but not squarefree numbers. It is clear that cubefree perfect squares are omitted from their table because on p. 328 they assert that Q((k^2)^(1/3)) = Q(k^(1/3)).
REFERENCES
Şaban Alaca & Kenneth S. Williams, Introductory Algebraic Number Theory. Cambridge: Cambridge University Press (2004): 325-329, Examples 12.6.8 & 12.6.9, Table 9.
LINKS
Lawrence C. Washington, Class Numbers of the Simplest Cubic Fields, Mathematics of Computation, Vol. 48, No. 177 (January 1987): 371 - 384.
EXAMPLE
a(8) = 1 because the eighth cubefree number is 9 and Q(9^(1/3)) has class number 1.
a(9) = 2 because the ninth cubefree number is 10 and Q(10^(1/3)) has class number 2.
CROSSREFS
Sequence in context: A364683 A270572 A095276 * A089338 A356400 A153066
KEYWORD
nonn,more
AUTHOR
Alonso del Arte, Aug 26 2014
STATUS
approved

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Last modified March 28 08:22 EDT 2024. Contains 371236 sequences. (Running on oeis4.)