A246457 Given m the n-th cubefree number, A004709(n); a(n) is the class number of field Q(m^(1/3)).

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

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

Table of n, a(n) for n=1..62.

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

Cf. A004709, A005472, A242867.

Sequence in context: A364683 A270572 A095276 * A089338 A356400 A153066

Adjacent sequences: A246454 A246455 A246456 * A246458 A246459 A246460

Keyword

nonn,more

Author

Alonso del Arte, Aug 26 2014

Status

approved