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%I #11 Feb 20 2021 11:02:29
%S 1,2,2,4,3,6,4,7,4,6,3,10,3,7,6,9,3,10,3,10,7,6,3,15,5,6,6,11,3,14,3,
%T 11,6,6,8,16,3,6,6,15,3,15,3,10,10,6,3,19,6,10,6,10,3,14,7,16,6,6,3,
%U 22,3,6,11,13,7,14,3,10,6,15,3,23,3,6,10,10,8,14,3,19,8,6,3,23,7
%N Number of isohedral Voronoi parallelotopes in R^n.
%H Marjorie Senechal, <a href="https://doi.org/10.1007/978-3-662-02838-4_10">Introduction to lattice geometry</a>. In M. Waldschmidt et al., eds., From Number Theory to Physics, pp. 476-495. Springer, Berlin, Heidelberg, 1992. See Cor. 3.7.
%F a(n) = d(n)+A321013(n)+A321014(n), where d(n) =A000005(n) is the number of divisors of n.
%e Of the five different Voronoi cells of 3-dimensional lattices, only two are isohedral, so a(3) = 2: the cube and the rhombic dodecahedron, the Voronoi cells of the primitive cubic and the face-centered cubic lattices.
%p d2:=proc(n) local c; if n <= 3 then return(0); fi;
%p c:=NumberTheory[tau](n)-1;
%p if (n mod 2)=0 then c:=c-1; fi;
%p if (n mod 3)=0 then c:=c-1; fi; c; end; # A321014
%p d3:=proc(n) local c; c:=0;
%p if (n mod 6)=0 then c:=c+1; fi;
%p if (n mod 7)=0 then c:=c+1; fi;
%p if (n mod 8)=0 then c:=c+1; fi; c; end; # A321013
%p [seq(NumberTheory[tau](n)+d2(n)+d3(n),n=1..120)];
%Y Cf. A000005, A321013, A321014, A071880, A071881, A071882.
%K nonn
%O 1,2
%A _N. J. A. Sloane_, Nov 04 2018
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