

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
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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

Table of n, a(n) for n=1..70.
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] (* JeanFrançois 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

Cf. A007503.
Sequence in context: A021877 A278713 A200623 * A232635 A201296 A246954
Adjacent sequences: A248668 A248669 A248670 * A248672 A248673 A248674


KEYWORD

nonn


AUTHOR

Nandor Sieben, Oct 11 2014


EXTENSIONS

a(23)a(70) from Andrew Howroyd, Jul 02 2018


STATUS

approved



