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A253598
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
399, 399, 935, 399, 935, 2015, 935, 399, 399, 4991, 51359, 2015, 8855, 1584599, 9486399, 20705, 5719, 18095, 2915, 935, 399, 46079, 162687, 2015, 22847, 46079, 16719263, 8855, 12719, 7055, 935, 80189, 189099039, 104663, 20705, 482143, 196559, 60059, 30073928079, 90287, 8855, 31535
OFFSET
1,1
COMMENTS
a(933) <= 266336887317945807999. - Daniel Suteu, Dec 01 2023
LINKS
Daniel Suteu, Table of n, a(n) for n = 1..932 (first 95 terms from Tim Johannes Ohrtmann, terms 96..154 from Robert G. Wilson v)
EXAMPLE
a(12) = 8855 because this is the least Lucas-Carmichael number which is divisible by A255602(12) = 35.
MATHEMATICA
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
a(96) from Charles R Greathouse IV, Feb 12 2015
STATUS
approved