A216325 Number of divisors of the degree of the minimal polynomial for 2*cos(Pi/n), n >= 1.

1, 1, 1, 2, 2, 2, 2, 3, 2, 3, 2, 3, 4, 4, 3, 4, 4, 4, 3, 4, 4, 4, 2, 4, 4, 6, 3, 6, 4, 4, 4, 5, 4, 5, 6, 6, 6, 6, 6, 5, 6, 6, 4, 6, 6, 4, 2, 5, 4, 6, 5, 8, 4, 6, 6, 8, 6, 6, 2, 5, 8, 8, 6, 6, 8, 6, 4, 6, 4, 8, 4, 8, 9, 9, 6, 9, 8, 8, 4, 6, 4, 8, 2, 8, 6, 8, 6, 8, 6, 8, 9, 6, 8, 4, 9, 6, 10, 8

Offset: 1

Author

Wolfdieter Lang, Sep 27 2012

Keywords

• nonn

Comments

For the minimal polynomials C(n,x) of the algebraic number rho = 2*cos(Pi/n), n >= 1, see their coefficient table A187360. Their degree is delta(n)= phi(2*n)/2, if n >= 2, and delta(1) = 1, with Euler's totient A000010. The delta sequence is given in A055034. a(n) is the number of divisors of delta(n).

a(n) is also the number of distinct Modd n orders given in the table A216320 in row n. (For Modd n see a comment on A203571).

See the analog A062821(n), with the number of divisors of phi(n). The corresponding order table is A216327.

Examples

			a(8) = 3 because C(8,x) = x^4 - 4*x^2 + 2, with degree delta(8) = A055034(8) = 4, and the three divisors of 4 are 1, 2 and 4. tau(4) = A000005(4) = 3.
		

Crossrefs

Cf. A062821 (analog).

Formula

a(n) = tau(delta(n)), n >= 1, with tau = A000005 (number of divisors), delta defined in a comment above and given as delta(n) = A055034(n).