|
|
A248671
|
|
Number of subgroups of the dihedral group Dn that are intersections of some maximal subgroups.
|
|
0
|
|
|
1, 4, 5, 4, 7, 15, 9, 4, 5, 21, 13, 15, 15, 27, 27, 4, 19, 15, 21, 21, 35, 39, 25, 15, 7, 45, 5, 27, 31, 79, 33, 4, 51, 57, 51, 15, 39, 63, 59, 21, 43, 103, 45, 39, 27, 75, 49, 15, 9, 21, 75, 45, 55, 15, 75, 27, 83, 93, 61, 79, 63, 99, 35, 4, 87, 151, 69, 57, 99, 151
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
Maximal subgroups are counted.
Smallest such subgroup is the Frattini subgroup.
These subgroups are called intersection subgroups in Ernst and Sieben link.
|
|
LINKS
|
|
|
FORMULA
|
|
|
MATHEMATICA
|
a[n_] := With[{f = FactorInteger[n][[All, 1]]}, Sum[d+1, {d, Divisors[Times @@ f]}]-1];
|
|
PROG
|
(GAP)
for n in [1..22] do
G:=DihedralGroup(2*n);
Ge:=Elements(G);
mse:=List(MaximalSubgroups(G), s->List(s, el->Position(Ge, el)));
C:=Combinations(mse);
Remove(C, 1); # empty intersection is removed
I:=List(C, Intersection);
Sort(I);
I:=Unique(I);
Print(Size(I), ", ");
od;
(PARI) a(n) = my(f=factor(n)[, 1]); sumdiv(prod(i=1, #f, f[i]), d, d+1 ) - 1; \\ Andrew Howroyd, Jul 02 2018
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|