A216326 Number of divisors of the degree of the minimal polynomial of 2*cos(Pi/prime(n)), with prime = A000040, n >= 1.

1, 1, 2, 2, 2, 4, 4, 3, 2, 4, 4, 6, 6, 4, 2, 4, 2, 8, 4, 4, 9, 4, 2, 6, 10, 6, 4, 2, 8, 8, 6, 4, 6, 4, 4, 6, 8, 5, 2, 4, 2, 12, 4, 12, 6, 6, 8, 4, 2, 8, 6, 4, 16, 4, 8, 2, 4, 8, 8, 12, 4, 4, 6, 4, 12, 4, 8, 16, 2, 8, 10, 2, 4, 8, 8, 2, 4, 12, 12, 12, 4, 16, 4, 16, 4, 4, 12, 12, 8, 8, 2

Offset

1,3

Comments

See a comment on A216325 on the degree delta(n) = A055034(n) of the polynomial C(n,x) of 2*cos(Pi/n) (coefficients in A187360), Here n is prime.

For p prime, delta(p) = (p - 1)/2 if p > 2 and 1 if p = 2. a(n) is the number of divisors of delta(prime(n)), with prime(n) = A000040(n).

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

See also A008328 for the mod p analog of this sequence.

Links

Table of n, a(n) for n=1..91.

Formula

a(n) = tau(delta(prime(n))), n>=1, with tau = A000005 (number of divisors), delta = A055034 and prime = A000040.

Example

a(6) = 4 because prime(6) = 13, and row n=13 of A216320 is [1  3  2  6  3  6] with 4 distinct numbers (Modd 13 orders).

Prog

(PARI) delta(n) = if (n==1, 1, eulerphi(2*n)/2); \\ A055034
a(n) = numdiv(delta(prime(n))); \\ Michel Marcus, Sep 12 2023

Crossrefs

Cf. A000005, A055034, A000040.

Cf. A187360, A216320, A216325, A008328 (mod p analog).

Sequence in context: A259981 A391066 A070705 * A381749 A101909 A215676

Adjacent sequences: A216323 A216324 A216325 * A216327 A216328 A216329

Keyword

nonn

Author

Wolfdieter Lang, Sep 27 2012

Status

approved