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A197366
Number of Abelian groups of order 2n which are isomorphic with the group of units of the ring Z/kZ for some k.
1
1, 2, 1, 2, 1, 2, 0, 3, 1, 2, 1, 2, 0, 1, 1, 4, 0, 3, 0, 3, 1, 1, 1, 3, 0, 1, 1, 1, 1, 2, 0, 5, 1, 0, 1, 5, 0, 0, 1, 3, 1, 1, 0, 3, 0, 1, 0, 5, 0, 1, 1, 1, 1, 3, 1, 3, 0, 1, 0, 2, 0, 0, 1, 5, 1, 1, 0, 1, 1, 1, 0, 6, 0, 1, 1, 0, 0, 2, 0, 5, 1, 1, 1, 2, 0, 1
OFFSET
1,2
FORMULA
a(n) = A101872(n) - A179229(n).
PROG
(GAP)
B:=[]; LoadPackage("sonata");
for m in [1..86] do
n := 2*m; S:=[];
for i in DivisorsInt(n)+1 do
if IsPrime(i)=true then
S:=Concatenation(S, [i]);
fi;
od;
T:=[];
for k in [1..Size(S)] do
T:=Concatenation(T, [S[k]/(S[k]-1)]);
od;
max := n*Product(T); R:=[];
for r in [1..Int(max)] do
if Phi(r)=n then
R:=Concatenation(R, [r]);
fi;
od;
A:=[];
for t in [1..NrSmallGroups(n)] do
if IsAbelian(SmallGroup(n, t))=true then
A:=Concatenation(A, [SmallGroup(n, t)]);
fi;
od;
U:=[];
for s in [1..Size(R)] do
U:=Concatenation(U, [Units(Integers mod R[s])]);
od;
V:=[];
for v in [1..Size(A)] do
for w in [1..Size(U)] do
if IsIsomorphicGroup(A[v], U[w])=true then
V:=Concatenation(V, [v]);
break;
fi;
od;
od;
B:=Concatenation(B, [Size(V)]);
od;
Print(B); # Miles Englezou, Oct 22 2024
CROSSREFS
Sequence in context: A350223 A274820 A230583 * A245715 A337736 A047885
KEYWORD
nonn,changed
AUTHOR
Artur Jasinski, Oct 14 2011
EXTENSIONS
Name corrected by Andrey Zabolotskiy, Oct 21 2024
Terms a(17) onwards from Miles Englezou, Oct 22 2024
STATUS
approved