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a(n) = least Lucas-Carmichael number which is divisible by b(n), where {b(n)} (A255602) is the list of all numbers which could be a divisor of a Lucas-Carmichael number.
3

%I #56 Dec 01 2023 08:32:59

%S 399,399,935,399,935,2015,935,399,399,4991,51359,2015,8855,1584599,

%T 9486399,20705,5719,18095,2915,935,399,46079,162687,2015,22847,46079,

%U 16719263,8855,12719,7055,935,80189,189099039,104663,20705,482143,196559,60059,30073928079,90287,8855,31535

%N a(n) = least Lucas-Carmichael number which is divisible by b(n), where {b(n)} (A255602) is the list of all numbers which could be a divisor of a Lucas-Carmichael number.

%C a(933) <= 266336887317945807999. - _Daniel Suteu_, Dec 01 2023

%H Daniel Suteu, <a href="/A253598/b253598.txt">Table of n, a(n) for n = 1..932</a> (first 95 terms from Tim Johannes Ohrtmann, terms 96..154 from Robert G. Wilson v)

%e a(12) = 8855 because this is the least Lucas-Carmichael number which is divisible by A255602(12) = 35.

%t LucasCarmichaelQ[n_] := Block[{fi = FactorInteger@ n}, ! PrimeQ@ n && Times @@ (Last@# & /@ fi) == 1 && Plus @@ Mod[n + 1, 1 + First@# & /@ fi] == 0]; LucasCarmichaelQ[1] = False; fQ[n_] := Block[{fi = FactorInteger@ n}, ffi = First@# & /@ fi; Times @@ (Last@# & /@ fi) == 1 && Min@ Flatten@ Table[Mod[1 + ffi, i], {i, ffi}] > 0]; fQ[1] = True; fQ[2] = False; lcdv = Select[ Range@ 3204, fQ]; f[n_] := Block[{k = lcdv[[n]]}, d = 2k; While[ !LucasCarmichaelQ@ k, k += d]; k]; Array[f, 95] (* _Robert G. Wilson v_, Feb 11 2015 *)

%Y Cf. A006972, A253597, A255602.

%K nonn

%O 1,1

%A _Tim Johannes Ohrtmann_, Jan 05 2015

%E a(96) from _Charles R Greathouse IV_, Feb 12 2015