OFFSET
1,2
COMMENTS
REFERENCES
Mohammad K. Azarian, On the Hyperfactorial Function, Hypertriangular Function, and the Discriminants of Certain Polynomials, International Journal of Pure and Applied Mathematics, Vol. 36, No. 2, 2007, pp. 251-257. Mathematical Reviews, MR2312537. Zentralblatt MATH, Zbl 1133.11012.
FORMULA
a(n) = (n^delta(n))/Discriminant(C(n,x)), n>=1, with the minimal polynomials C(n,x) of 2*cos(Pi/n), with coefficient triangle given in A187360, and their degree delta(n) given in A055034(n).
a(1) = 1. Conjectures for a(n), n>=2: i) a(2^k) = 2, k>=1;
ii) a(p^k) = p^((p^(k-1)+1)/2), for odd prime p and k>=1;
iii) a(n) = product(p^(delta(n)/(p-1)), odd p|n) otherwise.
EXAMPLE
a(30) = 30^delta(30)/A193681(30) = 30^8/324000000 = 2025.
For the conjectures: i) a(4) = 2; ii) a^(3^2) = a(9) = 3^((3+1)/2) = 9; iii) a(30) = a(2*3*5) = 3^(delta(30)/2)*5^(delta(30)/4) = 3^4*5^2 = 2025;
a(40) = a(2^3*5) = 5^(delta(40)/4) = 5^4 = 625; a(45) = a(3^2*5) = 3^(delta(45)/2)* 5^(delta(45)/4) = 91125.
CROSSREFS
KEYWORD
nonn
AUTHOR
Wolfdieter Lang, Aug 24 2012
STATUS
approved