%I A009490
%S A009490 1,1,2,3,4,6,6,9,11,14,16,20,23,27,31,35,43,47,55,61,70,78,88,98,111,123,
%T A009490 136,152,168,187,204,225,248,271,296,325,356,387,418,455,495,537,581,629,
%U A009490 678,732,787,851,918,986,1056,1133,1217,1307,1399,1498,1600,1708,1823
%N A009490 Number of distinct orders of permutations of n objects; number of nonisomorphic 
               cyclic subgroups of symmetric group S_n.
%C A009490 Also number of different lcm's of partitions of n.
%H A009490 T. D. Noe, <a href="b009490.txt">Table of n, a(n) for n=0..1000</a>
%H A009490 <a href="Sindx_Lc.html#lcm">Index entries for sequences related to lcm's</
               a>
%F A009490 Sum(b(k), k=0..n), where b(k) is the number of partitions of k into distinct 
               prime power parts (1 excluded) (A051613) - Vladeta Jovovic (vladeta(AT)eunet.rs)
%F A009490 G.f.: Prod(p prime, 1 + Sum(k >= 1, x^(p^k))) / (1-x) - David W. Wilson 
               (davidwwilson(AT)comcast.net), Apr 19, 2000
%t A009490 Table[ Length[ Union[ Apply[ LCM, Partitions[ n ], 1 ] ] ], {n, 30} ]
%Y A009490 Cf. A051613, A000792, A000793, A034891.
%Y A009490 Sequence in context: A073061 A006874 A034890 this_sequence A064778 A028335 
               A007464
%Y A009490 Adjacent sequences: A009487 A009488 A009489 this_sequence A009491 A009492 
               A009493
%K A009490 nonn,nice,easy
%O A009490 0,3
%A A009490 David W. Wilson (davidwwilson(AT)comcast.net)