A248671 Number of subgroups of the dihedral group Dn that are intersections of some maximal subgroups.
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
Offset: 1
Keywords
Links
- Dana C. Ernst, Nandor Sieben, Impartial achievement and avoidance games for generating finite groups, arXiv:1407.0784 [math.CO], 2014.
Crossrefs
Cf. A007503.
Programs
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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;
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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 *) -
PARI
a(n) = my(f=factor(n)[,1]); sumdiv(prod(i=1, #f, f[i]), d, d+1 ) - 1; \\ Andrew Howroyd, Jul 02 2018
Formula
a(n) = A007503(n) - 1 for squarefree n. - Andrew Howroyd, Jul 02 2018
Extensions
a(23)-a(70) from Andrew Howroyd, Jul 02 2018
Comments