cp's OEIS Frontend

A335887 Maximal sum of subgroup orders for a finite group of order n.

%I A335887 #11 Jun 28 2020 18:54:15
%S A335887 1,3,4,11,6,16,8,51,22,26,12,60,14,36,24,307,18,130,20,98,50,56,24,
%T A335887 284,56,66,184,136,30,144,32,2451,48,86,48,498,38,96,92,466,42,200,44,
%U A335887 212,132,116,48,1740,106,456,72,250,54,1696,122,648,134,146,60,552,62
%N A335887 Maximal sum of subgroup orders for a finite group of order n.
%D A335887 The GAP Group, GAP - Groups, Algorithms, and Programming, Version 4.9.3, 2018. gap-system.org.
%H A335887 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 A335887 (GAP)
%o A335887 L:=[];;
%o A335887 for n in [1..100] do
%o A335887   Mn:=0;
%o A335887   r:=NrSmallGroups(n);
%o A335887   for d in [1..r] do
%o A335887     g:=SmallGroup(n,d);
%o A335887     lat:=AllSubgroups(g);
%o A335887     sg:=Sum(List(lat,Order));
%o A335887     if sg>Mn then
%o A335887       Mn:=sg;
%o A335887     fi;
%o A335887   od;
%o A335887   Add(L,Mn);
%o A335887 od;
%o A335887 Print(L);
%Y A335887 Cf. A000005, A000203, A018216, A335888.
%K A335887 nonn
%O A335887 1,2
%A A335887 _Sébastien Palcoux_, Jun 28 2020