A379423 Least modulus k such that the multiplicative group modulo k is the direct product of n nontrivial cyclic groups.

1, 3, 7, 21, 56, 168, 504, 1736, 5208, 15624, 57288, 171864, 671832, 2234232, 7390152, 32023992, 96071976, 450799272, 1559322072, 5860390536, 20271186936, 95118646392, 385152551784, 1236542403096, 6182712015480, 23494305658824, 82848341007432, 409295535424776

Offset: 0

Author

Asher Gray, Dec 22 2024

Keywords

• nonn

Comments

Compare with A102476. That sequence also measures the least modulus k with n nontrivial cyclic groups, but only using the rank, the minimal representation for each such k. For example, A102476(3) = 24 as (Z/24Z)* ≅ C2 x C2 x C2. However with this sequence a(3) = 21 as (Z/21Z)* ≅ C2 x C2 x C3.

Examples

			a(2) = 7 because (Z/7Z)* ≅ C2 x C3.
		

Links

• Asher Gray, Table of n, a(n) for n = 0..1000
• Asher Gray, Least modulus with n cycles, Github repository.
• Asher Gray, Sequences from Group Theory, YouTube Video.

Crossrefs

Cf. A102476.