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

0,2

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.

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.

Example

a(2) = 7 because (Z/7Z)* ≅ C2 x C3.

Crossrefs

Cf. A102476.

Sequence in context: A151267 A319558 A307251 * A320803 A262184 A091489

Adjacent sequences: A379420 A379421 A379422 * A379424 A379425 A379426

Keyword

nonn

Author

Asher Gray, Dec 22 2024

Status

approved