A060015 - OEIS

%I #15 Oct 14 2023 13:19:13

%S 1,1,7,31,211,1411,12601,137047,1516831,18111751,223179001,2973194071,

%T 46287964867,835826439631,15722804528341,292673102609791,

%U 5177400032329231,102538737981192607,2284570602107946601

%N Sum of orders of all even permutations of n letters.

%H Joshua Harrington, Lenny Jones, and Alicia Lamarche, <a href="http://dx.doi.org/10.1155/2014/835125">Characterizing Finite Groups Using the Sum of the Orders of the Elements</a>, International Journal of Combinatorics, Volume 2014, Article ID 835125, 8 pages.

%e For n = 4 there is 1 even permutation (1) of order 1, 3 even permutations (12)(34) etc. of order 2 and 8 (123) etc. of order 3, for a total of 31.

%t g[list_]:=Total[list]!/Apply[Times,list]/Apply[Times,Table[Count[list,n]!,{n,1,20}]];f[list_]:=Apply[Plus,Table[Count[list,n],{n,2,20,2}]];Map[Total,Table[Map[g,Select[Partitions[n],EvenQ[f[#]]&]]*Map[Apply[LCM,#]&,Select[Partitions[n],EvenQ[f[#]]&]],{n,1,20}]]  (* _Geoffrey Critzer_, Mar 26 2013 *)

%Y Cf. A060014.

%K nonn,nice,easy

%O 1,3

%A _N. J. A. Sloane_, Mar 17 2001

%E More terms from _Vladeta Jovovic_, Mar 18 2001