A253597 -id:A253597 - cp's OEIS frontend

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

Tim Johannes Ohrtmann, Jan 05 2015

nonn

a(933) <= 266336887317945807999. - Daniel Suteu, Dec 01 2023

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

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)

Cf. A006972, A253597, A255602.

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 *)

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

A299213 Lucas-Carmichael numbers whose prime factors do not divide any smaller Lucas-Carmichael number.

Original entry on oeis.org

399, 935, 565861139, 5778659039, 22824172799, 49569379679, 221511111527, 572531110799, 745012846679

Offset: 1

Tim Johannes Ohrtmann, Feb 05 2018

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

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

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

Cf. A006972, A202562, A253597.

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])))

cp's OEIS Frontend

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.

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