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
Dana C. Ernst, Nandor Sieben, Impartial achievement and avoidance games for generating finite groups, arXiv:1407.0784 [math.CO], 2014.
FORMULA
a(n) = A007503(n) - 1 for squarefree n. - Andrew Howroyd, Jul 02 2018
MATHEMATICA
a[n_] := With[{f = FactorInteger[n][[All, 1]]}, Sum[d+1, {d, Divisors[Times @@ f]}]-1];
Array[a, 70] (* Jean-François Alcover, Aug 29 2018, after Andrew Howroyd *)
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
Nandor Sieben, Oct 11 2014
EXTENSIONS
a(23)-a(70) from Andrew Howroyd, Jul 02 2018
STATUS
approved