|
%I #15 Jun 30 2017 09:54:57
%S 2465,278545,13696033,75151441,93869665,169570801,490099681,612347905,
%T 707926801,744866305,1190790721,1321983937,1913016001,2159003281,
%U 2176838049,2232385345,2353639681,3880251649,4059151489,4314912001,5204110465,8355729313,8548543585,9584174881,10054063041,10933377841
%N Carmichael numbers divisible by 17 and 29.
%C Conjecture: Any Carmichael number C divisible by 17 and 29 can be written as C = 952*n + 561; checked up to the Carmichael number 105823343809.
%C Note: the number 561 is the first Carmichael number and the number 952 comes from the following interesting relation: 952^2 = 1105^2 - 561^2 (where 1105 is the second Carmichael number).
%C The conjecture follows from Korselt's criterion. More is true: a(n) = 2465 mod 55216. - _Charles R Greathouse IV_, Oct 02 2012
%H Charles R Greathouse IV, <a href="/A182381/b182381.txt">Table of n, a(n) for n = 1..10000</a>
%H E. W. Weisstein, <a href="http://mathworld.wolfram.com/CarmichaelNumber.html">Carmichael Number</a>
%o (PARI) Korselt(n)=my(f=factor(n)); for(i=1, #f[, 1], if(f[i, 2]>1||(n-1)%(f[i, 1]-1), return(0))); 1
%o list(lim)=my(v=List()); forstep(n=2465, lim, 55216, if(Korselt(n), listput(v, n))); Vec(v) \\ _Charles R Greathouse IV_, Jun 30 2017
%K nonn
%O 1,1
%A _Marius Coman_, Apr 27 2012
%E Terms corrected by _Charles R Greathouse IV_, Oct 02 2012
|
