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.

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(640) <= 2172140962024052891965613396799. - Daniel Suteu, Feb 25 2023

Links

Daniel Suteu, Table of n, a(n) for n = 1..639 (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

Cf. A006972, A253597, A255602.

Sequence in context: A235569 A261768 A274446 * A046013 A352360 A176911

Adjacent sequences: A253595 A253596 A253597 * A253599 A253600 A253601

Keyword

nonn

Author

Tim Johannes Ohrtmann, Jan 05 2015

Extensions

a(96) from Charles R Greathouse IV, Feb 12 2015

Status

approved