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
Keywords
References
- The GAP Group, GAP - Groups, Algorithms, and Programming, Version 4.9.3, 2018. gap-system.org.
Links
- Sébastien Palcoux, On the sum the subgroup orders of a finite group (version: 2020-06-29), MathOverflow.
Programs
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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);