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A210845
Values n for which A055034(n) is squarefree.
2
1, 2, 3, 4, 5, 6, 7, 9, 11, 13, 14, 18, 21, 22, 23, 25, 29, 31, 33, 43, 46, 47, 49, 53, 59, 61, 62, 67, 69, 71, 77, 79, 83, 86, 93, 94, 98, 99, 103, 107, 118, 121, 129, 131, 134, 139, 141, 142, 147, 149, 157, 158, 161, 166, 167, 169, 173, 177, 179, 191
OFFSET
1,2
COMMENTS
A055034(n) is the degree delta(n) of the minimal polynomial of the algebraic number rho(n):=2*cos(pi/n), n>=1, whose coefficients are shown in A187360. It is also the order of multiplicative abelian group Modd n (for multiplication Modd n see a comment on A203571). This is the Galois group Gal(Q(rho(n))/Q). If the number of abelian groups of order delta(n) is 1 then this group is necessarily cyclic.
Because A000688 is 1 exactly for the squarefree numbers A005117, the set of a(n) values of the present sequence is a (proper) subset of A206551. Hence it is immediately clear that the multiplicative group Modd a(n) is cyclic, but there are other cyclic Modd n groups, e.g., for n = 8, 10, 15, 16, 17, 19, 26, 27, 32, 34, 35, 37, 38, 39, 41,...
FORMULA
A055034(a(n)) is squarefree, i.e. from A005117.
EXAMPLE
a(3)=3 because delta(3)=A055034(3)= 1, and 1 is a member of the squarefree numbers A005117.
a(8)=9 because A055034(9)= 3 = A005117(3).
a(10)=13 because A055034(13)= 6 = A005117(5).
CROSSREFS
Cf. A206551.
Sequence in context: A363938 A032957 A362132 * A057202 A277417 A246885
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Apr 11 2012
STATUS
approved