A210845 Values n for which A055034(n) is squarefree.

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

Author

Wolfdieter Lang, Apr 11 2012

Keywords

• nonn
• easy

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,...

Examples

			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.

Formula

A055034(a(n)) is squarefree, i.e. from A005117.