OFFSET
1,2
COMMENTS
Powers of 4 cannot appear in this sequence. This is because for a group of order p^n, the number of subgroups of order p^k is congruent to 1 mod p, for 0 <= k <= n. It follows from p=2 and Lagrange's theorem that the number of subgroups of order 2^n for n even is congruent to 1 mod 2, i.e. not equal to 2^n. - Robin Jones, Feb 17 2024
a(33) >= 512. The smallest term strictly larger than 512 is 560. -Robin Jones, Feb 18 2024
EXAMPLE
1 is a term since the trivial group (order 1) has exactly 1 subgroup.
2 is a term since the cyclic group C_2 has exactly 2 subgroups.
6 is a term since the symmetric group S_3 has exactly 6 subgroups.
PROG
(Magma, to get the terms up to 100)
i:=1;
while i lt 100 do // terms up to 100
for G in SmallGroups(i) do
if #AllSubgroups(G) eq i then
i; break;
end if;
; end for;
i:=i+1;
end while;
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Robin Jones, Dec 29 2023
STATUS
approved