A335888 Maximal sum of subgroup indices for a finite group of order n.

1, 3, 4, 11, 6, 18, 8, 51, 22, 38, 12, 74, 14, 66, 24, 307, 18, 162, 20, 166, 74, 146, 24, 378, 56, 198, 184, 298, 30, 308, 32, 2451, 48, 326, 48, 722, 38, 402, 212, 886, 42, 564, 44, 682, 132, 578, 48, 2458, 106, 888, 72, 934, 54, 2268, 182, 1626, 422, 902, 60, 1444

Offset: 1

Author

Sébastien Palcoux, Jun 28 2020

Keywords

• nonn

References

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

Crossrefs

Cf. A000005, A000203, A018216, A335887.

Programs

GAP

L:=[];;
for n in [1..100] do
  Mn:=0;
  r:=NrSmallGroups(n);
  for d in [1..r] do
    g:=SmallGroup(n,d);
    lat:=AllSubgroups(g);
    sg:=Sum(List(lat, h->Order(g)/Order(h)));
    if sg>Mn then
      Mn:=sg;
    fi;
  od;
  Add(L,Mn);
od;
Print(L);