A299213 - OEIS

%I #13 Mar 29 2026 08:59:27

%S 399,935,565861139,5778659039,22824172799,49569379679,221511111527,

%T 572531110799,745012846679,1034101753931,1370873302991,2170525568639,

%U 2374771783151,2621128819063,3371253685379,3720157305479,5533009370111,5850130431599,8405935805119,8454421987199

%N Lucas-Carmichael numbers whose prime factors do not divide any smaller Lucas-Carmichael number.

%C Also numbers whose number of occurrence in A253597 equals the number of their prime factors.

%C All known terms have only 3 prime factors. Does any term with more than 3 prime factors exist?

%H Amiram Eldar, <a href="/A299213/b299213.txt">Table of n, a(n) for n = 1..105</a> (terms below 10^15, calculated from Daniel Suteu's file at A006972)

%e 565861139 = 193*1163*2521 and no smaller Lucas-Carmichael number is divisible by 193, 1163 or 2521.

%o (PARI) a=readvec("b006972.txt"); print1(399); for(b=2,10000, e=true; f=factor(a[b]); for(d=1,#f[, 1], for(c=1,b-1, if(a[c]%f[d,1]==0, e=false))); if(e==true, print1(", ",a[b])))

%Y Cf. A006972, A202562, A253597.

%K nonn

%O 1,1

%A _Tim Johannes Ohrtmann_, Feb 05 2018

%E a(10)-a(20) from _Amiram Eldar_, Mar 29 2026