A074270 - OEIS

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

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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 1060000.

a(11), if it exists, exceeds 7500000. - Sean A. Irvine, Jan 22 2025

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: A266211 A372793 A363920 * A254522 A007120 A092973

Adjacent sequences: A074267 A074268 A074269 * A074271 A074272 A074273

KEYWORD

nonn,more

AUTHOR

Don Reble, Sep 20 2002

STATUS

approved