%I #11 Jun 28 2020 18:54:15

%S 1,3,4,11,6,16,8,51,22,26,12,60,14,36,24,307,18,130,20,98,50,56,24,

%T 284,56,66,184,136,30,144,32,2451,48,86,48,498,38,96,92,466,42,200,44,

%U 212,132,116,48,1740,106,456,72,250,54,1696,122,648,134,146,60,552,62

%N Maximal sum of subgroup orders for a finite group of order n.

%D The GAP Group, GAP - Groups, Algorithms, and Programming, Version 4.9.3, 2018. gap-system.org.

%H Sébastien Palcoux, <a href="https://mathoverflow.net/q/364368/34538">On the sum the subgroup orders of a finite group</a> (version: 2020-06-29), MathOverflow.

%o (GAP)

%o L:=[];;

%o for n in [1..100] do

%o Mn:=0;

%o r:=NrSmallGroups(n);

%o for d in [1..r] do

%o g:=SmallGroup(n,d);

%o lat:=AllSubgroups(g);

%o sg:=Sum(List(lat,Order));

%o if sg>Mn then

%o Mn:=sg;

%o fi;

%o od;

%o Add(L,Mn);

%o od;

%o Print(L);

%Y Cf. A000005, A000203, A018216, A335888.

%K nonn

%O 1,2

%A _Sébastien Palcoux_, Jun 28 2020