This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A292368 #6 Sep 17 2017 22:51:06
%S A292368 1,21,55,385,49105,136081,701569,2830465,7996801,29158921,49268737,
%T A292368 52617601
%N A292368 Numbers n with record number of primes p such that n*p is a Lucas-Carmichael number.
%C A292368 Given a number n and a prime number p such that n*p is a Lucas-Carmichael number, then (p+1)|(n-1), so the number of prime solution p given n is bounded by the number of divisors of (n-1).
%C A292368 The number of solutions is 0, 1, 2, 4, 5, 6, 7, 8, 10, 13, 15, 32.
%e A292368 21 has one prime number, 19, such that 21*19 = 399 is a Lucas-Carmichael number. 55 has 2 prime numbers, 17 and 53, such that 55*17 = 935 and 55*53 = 2915 are Lucas-Carmichael numbers.
%t A292368 lucasCarmichaelQ[n_]:=!PrimeQ[n] && Union[Transpose[FactorInteger[n]][[2]]] == {1} && Union[Mod[n + 1, Transpose[FactorInteger[n]][[1]]+1]]=={0};
%t A292368 numSol[n_]:=Module[{m = 0}, ds = Divisors[n-1]; Do[p = ds[[k]]-1; If[!PrimeQ[p], Continue[]]; If[! lucasCarmichaelQ[p*n], Continue[]]; m++, {k, 1, Length[ds]}]; m]; numSolmax = -1; seq = {}; nums = {};
%t A292368 Do[m = numSol[n]; If[m > numSolmax, AppendTo[seq, n]; AppendTo[nums, m]; Print[{n, m}]; numSolmax = m], {n, 1, 100000}]; seq
%Y A292368 Cf. A006972.
%K A292368 nonn,more
%O A292368 1,2
%A A292368 _Amiram Eldar_, Sep 15 2017