A380222 Highest integer k such that the multiplicative group modulo k is a subgroup of the symmetric group S_n.

2, 6, 6, 12, 18, 30, 42, 60, 90, 126, 210, 252, 420, 630, 840, 1260, 1680, 2730, 3276, 5460, 8190, 10920, 16380, 21840, 32760, 40950, 65520, 90090, 120120, 180180, 253890, 360360, 507780, 720720, 1015560, 1332240, 2031120, 2792790, 3996720, 5585580

Offset: 1

Author

Asher Gray, Jan 17 2025

Keywords

• nonn

Comments

a(n) is the highest k for which A380827(k) <= n.

Examples

			a(2) = 6 because (Z/6Z)* is a subgroup of S_2 (isomorphic to it in fact) and there is no modulus k with k > 6 and (Z/kZ)* a subgroup of S_2.
		

Links

• Asher Gray, Table of n, a(n) for n = 1..5000
• Asher Gray, Highest modulus within S_n, Github repository.

Crossrefs

Cf. A380827, A034891.