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A335887 Maximal sum of subgroup orders for a finite group of order n. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 20 09:06 EDT 2021. Contains 348099 sequences. (Running on oeis4.)