A383459 Minimum number of cycles in any permutation in S_n of the highest order (A000793(n)).

1, 1, 1, 1, 2, 1, 2, 2, 2, 3, 2, 3, 4, 3, 3, 3, 4, 3, 4, 5, 5, 4, 4, 5, 4

Offset: 1

Author

Anand Jain, Mar 22 2025

Keywords

• nonn
• more

Comments

Landau's function g(n) = A000793(n) gives the maximum order of any permutation on n elements.

The number of permutations of order g(n) is A074059, and the number of different cycle types of permutations of order g(n) is A074064. a(n) is the maximum number of cycles in any permutation of order g(n), and A383459(n) is the minimum number of cycles in any permutation of order g(n).

Examples

			There are two different cycle types of permutations in S_6 of the maximum order g(6) = 6, for example (123456) and (12)(345)(6). The minimum number of cycles is a(6) = 1 and maximum number is A383458(6) = 3.
		

Crossrefs

Cf. A000793, A074059, A074064, A383458.