A076584 Let P(n,x) = Product_{k=1..n} polcyclo(k,x) where polcyclo(k,x) denotes the k-th cyclotomic polynomial. Sequence gives the maximum value of coefficients of P(n,x).

1, 1, 1, 1, 3, 2, 9, 13, 28, 22, 174, 143, 1421, 1179, 965, 1627, 22543, 19720, 311514, 273894, 236320, 209255, 4127583, 3734824, 16283658, 14694118, 39214357, 35681217, 915568753, 847646751, 23431024516, 43093548356, 39165894190

Offset

1,5

Comments

The degree of P(n,x) is phi(1) + phi(2) + ... + phi(n) = A002088(n) and if c(n,i) denotes the coefficient of x^i in P(n,x): c(n,i) + c(n, A002088(n) - i) = 0.

Links

Table of n, a(n) for n=1..33.

Example

P(5,x) = x^10 + 2*x^9 + 3*x^8 + 3*x^7 + 2*x^6 - 2*x^4 - 3*x^3 - 3*x^2 - 2*x - 1, hence a(5)=3.

Prog

(PARI) a(n)=vecmax(vector(sum(k=1, n, eulerphi(k))+1, i, polcoeff(prod(i=1, n, polcyclo(i)), i-1)))

Crossrefs

Sequence in context: A077898 A303631 A358603 * A309673 A378931 A154343

Adjacent sequences: A076581 A076582 A076583 * A076585 A076586 A076587

Keyword

nonn

Author

Benoit Cloitre, Oct 20 2002

Status

approved