A074270 a(n) = the least positive number X such that Cn(X) is X-smooth, where Cn is the n-th cyclotomic polynomial and "X-smooth" means "has no prime factor greater than X".

2, 3, 16, 7, 2205, 17, 174037, 1600, 45796, 984

Offset

1,1

Comments

Inspired by a conjecture of David W. Wilson: for each nonzero polynomial P with integer coefficients, there is an integer X such that P(X) is X-smooth. Certain cyclotomic polynomials seem to stress the conjecture, but no refutation is yet known. If a(11) exists, it is greater than 1,060,000.

Links

Table of n, a(n) for n=1..10.

Example

a(5)=2205 because C5(2205) = 23650012729981 = 11*11*31*61*101*691*1481; and no prime factor is greater than 2205.

Crossrefs

Sequence in context: A066841 A266211 A363920 * A254522 A007120 A092973

Adjacent sequences: A074267 A074268 A074269 * A074271 A074272 A074273

Keyword

nonn

Author

Don Reble, Sep 20 2002

Status

approved