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


%S 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,

%T 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,

%U 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

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

%C 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).

%C 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).

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

%F 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).

%e 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.

%Y Cf. A062821 (analog).

%K nonn

%O 1,4

%A _Wolfdieter Lang_, Sep 27 2012

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Last modified September 30 10:18 EDT 2020. Contains 337439 sequences. (Running on oeis4.)