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A370421
Integers k such that all groups of order k have strictly fewer than k subgroups.
3
3, 5, 7, 9, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 25, 26, 29, 30, 31, 33, 34, 35, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 49, 51, 52, 53, 55, 57, 58, 59, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 82, 83, 85, 86, 87, 89, 91, 92, 93, 94, 95, 97, 99
OFFSET
1,1
COMMENTS
This sequence is infinite. All primes other than 2 appear in the sequence.
LINKS
PROG
(Magma) // to get the terms up to 1023. The program will not work for i=1024, returning a positive result, since those groups are not classified.
i:=1;
while i lt 1024 do // terms up to 1023
inSequence:=1;
j:=1;
while j le NumberOfSmallGroups(i) do //iterate through all the groups of order i
G:=SmallGroup(i, j);
if #AllSubgroups(G) ge i then //some group has >= i subgroups
inSequence:=0;
break;
end if;
j:=j+1;
end while;
if inSequence eq 1 then
i;
end if;
i:=i+1;
end while;
CROSSREFS
Sequence in context: A238524 A237287 A237046 * A076212 A085621 A324101
KEYWORD
nonn
AUTHOR
Robin Jones, Feb 18 2024
STATUS
approved