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

1, 3, 4, 11, 6, 16, 8, 51, 22, 26, 12, 60, 14, 36, 24, 307, 18, 130, 20, 98, 50, 56, 24, 284, 56, 66, 184, 136, 30, 144, 32, 2451, 48, 86, 48, 498, 38, 96, 92, 466, 42, 200, 44, 212, 132, 116, 48, 1740, 106, 456, 72, 250, 54, 1696, 122, 648, 134, 146, 60, 552, 62

Offset

1,2

References

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

Links

Table of n, a(n) for n=1..61.

Sébastien Palcoux, On the sum the subgroup orders of a finite group (version: 2020-06-29), MathOverflow.

Prog

(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, Order));
    if sg>Mn then
      Mn:=sg;
    fi;
  od;
  Add(L, Mn);
od;
Print(L);

Crossrefs

Cf. A000005, A000203, A018216, A335888.

Sequence in context: A295824 A180696 A133760 * A335888 A328851 A197953

Adjacent sequences: A335884 A335885 A335886 * A335888 A335889 A335890

Keyword

nonn

Author

Sébastien Palcoux, Jun 28 2020

Status

approved