A379424 Least modulus k such that the multiplicative group modulo k has a difference of n nontrivial cycles between its minimal and maximal representation.

1, 7, 31, 211, 1333, 6541, 45787, 281263, 1968841, 13781887, 93098053, 649998793, 4549991551, 31849940857, 215149600483, 1506047203381, 10542330423667, 86982188480467, 587573558919073, 4113014912433511, 28791104387034577, 247368468304929733

Offset

0,2

Comments

This is equal to the least modulus k such that (Z/kZ)* has a representation as a direct product of cyclic groups, of which n are odd cycles. The number of even cycles in the maximal representation is equal to the total cycles in the minimal representation.

Links

Asher Gray, Table of n, a(n) for n = 0..500

Asher Gray, Least modulus with n cycles, Github repository.

Asher Gray, Sequences from Group Theory, YouTube Video.

Example

a(4) = 1333 because (Z/1333Z) ≅ C210 x C6 ≅ C2 x C3 x C5 x C2 x C3 x C7. The first representation has 2 cycles and the second has 6, a difference of 4.

Crossrefs

Cf. A102476, A379423.

Sequence in context: A155521 A201116 A329944 * A060015 A261558 A241456

Adjacent sequences: A379421 A379422 A379423 * A379425 A379426 A379427

Keyword

nonn

Author

Asher Gray, Dec 22 2024

Status

approved