A327721 Dimension of quantum lens space needed for non-uniqueness.

4, 6, 6, 4, 8, 6, 4, 6, 12, 4, 14, 8, 4, 6, 18, 4, 20, 6, 4, 12, 24, 4, 6, 14, 4, 6, 30, 4, 32, 6, 4, 18, 6, 4, 38, 20, 4, 6, 42, 4, 44, 6, 4, 24, 48, 4, 8, 6, 4, 6, 54, 4, 6, 6, 4, 30, 60, 4, 62, 32, 4, 6, 6, 4, 68, 6, 4, 6, 72, 4, 74, 38, 4, 6, 8, 4, 80, 6, 4, 42, 84, 4, 6

Offset

3,1

Comments

a(n) is the dimension of the quantum lens space compared to the primary parameter n for the isomorphism class to depend on secondary parameters. In the literature the primary parameter is usually denoted by r.

Links

Table of n, a(n) for n=3..85.

Peter Lunding Jensen, Frederik Ravn Klausen, Peter M. R. Rasmussen, Combinatorial classification of quantum lens spaces, arXiv:1701.04003 [math.OA], 2017; Pacific Journal of Mathematics, Vol. 297, No. 2, 12.2018, p. 339-365.

Formula

For n > 2, whenever 4 does not divide n we have a(n) = p + 1, where p is the smallest odd prime dividing n; and in the case 4 divides n we have a(n) = 4 whenever 3 divides n and a(n) = 6 otherwise.

Example

a(8) = 6 since 4 divides 8 and no odd primes do.
a(11) = 11+1 = 12 since the smallest odd prime dividing 11 is 11.
a(12) = 4 since 3 and 4 both divide 12.

Prog

(PARI) a(n) = {if (n % 4,  my(f=factor(n)[, 1]~); if (f[1] % 2, f[1]+1, f[2]+1), if (n%3, 6, 4)); } \\ Michel Marcus, Sep 26 2019

Crossrefs

Sequence in context: A200352 A286720 A201393 * A327268 A146208 A011227

Adjacent sequences: A327718 A327719 A327720 * A327722 A327723 A327724

Keyword

nonn

Author

Frederik Ravn Klausen, Sep 23 2019

Extensions

More terms from Michel Marcus, Sep 27 2019

Status

approved