

A292368


Numbers n with record number of primes p such that n*p is a LucasCarmichael number.


0



1, 21, 55, 385, 49105, 136081, 701569, 2830465, 7996801, 29158921, 49268737, 52617601
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OFFSET

1,2


COMMENTS

Given a number n and a prime number p such that n*p is a LucasCarmichael number, then (p+1)(n1), so the number of prime solution p given n is bounded by the number of divisors of (n1).
The number of solutions is 0, 1, 2, 4, 5, 6, 7, 8, 10, 13, 15, 32.


LINKS

Table of n, a(n) for n=1..12.


EXAMPLE

21 has one prime number, 19, such that 21*19 = 399 is a LucasCarmichael number. 55 has 2 prime numbers, 17 and 53, such that 55*17 = 935 and 55*53 = 2915 are LucasCarmichael numbers.


MATHEMATICA

lucasCarmichaelQ[n_]:=!PrimeQ[n] && Union[Transpose[FactorInteger[n]][[2]]] == {1} && Union[Mod[n + 1, Transpose[FactorInteger[n]][[1]]+1]]=={0};
numSol[n_]:=Module[{m = 0}, ds = Divisors[n1]; Do[p = ds[[k]]1; If[!PrimeQ[p], Continue[]]; If[! lucasCarmichaelQ[p*n], Continue[]]; m++, {k, 1, Length[ds]}]; m]; numSolmax = 1; seq = {}; nums = {};
Do[m = numSol[n]; If[m > numSolmax, AppendTo[seq, n]; AppendTo[nums, m]; Print[{n, m}]; numSolmax = m], {n, 1, 100000}]; seq


CROSSREFS

Cf. A006972.
Sequence in context: A083676 A264104 A236694 * A301607 A145719 A031963
Adjacent sequences: A292365 A292366 A292367 * A292369 A292370 A292371


KEYWORD

nonn,more


AUTHOR

Amiram Eldar, Sep 15 2017


STATUS

approved



