A020902 Number of nonisomorphic cyclic subgroups of alternating group A_n (or number of distinct orders of even permutations of n objects); number of different LCM's of partitions of n which have even number of even parts.

1, 1, 1, 2, 3, 4, 5, 7, 8, 11, 13, 16, 18, 22, 26, 30, 35, 39, 46, 51, 60, 67, 76, 84, 94, 105, 119, 133, 147, 162, 176, 196, 218, 240, 263, 286, 310, 340, 374, 409, 441, 476, 515, 559, 608, 662, 711, 762, 817, 883, 955, 1030, 1104, 1177, 1257, 1352, 1453, 1559

Offset: 0

Author

Vladeta Jovovic

Keywords

• nonn

Examples

			a(8)=8 because lcm{1^8} = 1, lcm{1^4 * 2^2, 2^4} = 2, lcm{1^5 * 3^1, 1^2 * 3^2} = 3, lcm{4^2, 1^2 * 2^1 * 4^1} = 4, lcm{1^3 * 5^1} = 5, lcm{2^1 * 6^1, 1^1 * 2^2 * 3^1} = 6, lcm{1^1 * 7^1} = 7, lcm{3^1 * 5^1} = 15.
		

References

• V. Jovovic, Some combinatorial characteristics of symmetric and alternating groups (in Russian), Belgrade, 1980, unpublished.

Crossrefs

Cf. A034891.

Formula

a(n) = A009490(n-2) + A035942(n-1) + A035942(n), n > 1, a(0)=a(1)=1.