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

Author

Asher Gray, Dec 22 2024

Keywords

• nonn

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.

Examples

			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.
		

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.

Crossrefs

Cf. A102476, A379423.