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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".
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%I #10 Jan 22 2025 03:31:51

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

%N 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".

%C 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.

%C a(11), if it exists, exceeds 7500000. - _Sean A. Irvine_, Jan 22 2025

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

%K nonn,more

%O 1,1

%A _Don Reble_, Sep 20 2002