

A137979


Highest coefficient occuring in the factorization of x^n  1 over the reals.


4



1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2
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OFFSET

1,105


COMMENTS

Based on a comment in Mathematica helpfile ref/Factor  Neat Examples.
The first factorization of x^n  1 in which a 2 appears as a coefficient is for n=105.


LINKS

N. J. A. Sloane, Table of n, a(n) for n = 1..10000


EXAMPLE

a(4) = 1 because x^4  1 = (x^2+1)(x+1)(x1) and the highest coefficient of these three terms is 1.
The first time a 2 appears is at n=105, where the factorization is:
(x1)*(x^6+x^5+x^4+x^3+x^2+x+1)*(x^4+x^3+x^2+x+1)*
(x^24x^23+x^19x^18+x^17x^16+x^14x^13+x^12x^11+x^10x^8+x^7x^6+x^5x+1)*
(x^2+x+1)*(x^12x^11+x^9x^8+x^6x^4+x^3x+1)*
(x^8x^7+x^5x^4+x^3x+1)*
(x^48+x^47+x^46x^43x^422*x^41x^40x^39+x^36+x^35+x^34+x^33+x^32+x^31x^28x^26x^24x^22x^20+x^17+x^16+x^15+x^14+x^13+x^12x^9x^82*x^7x^6x^5+x^2+x+1).  N. J. A. Sloane, Apr 18 2008


MATHEMATICA

Table[Max[Abs[Flatten[CoefficientList[Transpose[FactorList[x^i  1]][[1]], x]]]], {i, 1, 1000}]


CROSSREFS

Cf. A013590, A013594.
Sequence in context: A160338 A216579 A229878 A235145 A037281 A143241 A118626
Adjacent sequences: A137976 A137977 A137978 * A137980 A137981 A137982


KEYWORD

nonn


AUTHOR

Ian Miller, Feb 25 2008


STATUS

approved



