

A292366


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


0




OFFSET

1,2


COMMENTS

If n*p is a Carmichael number, where p is a prime, then (p1)(n1), so given n, the number of possible primes is bounded by the number of divisors of n1.
The corresponding number of solutions is 0, 1, 2, 3, 5, 7, 10, 12, 14.


LINKS

Table of n, a(n) for n=1..10.


EXAMPLE

33 has one prime number, 17, such that 33*17 = 561 is a Carmichael number. 85 has 2 prime numbers, 13 and 29, such that 85*13 = 1105 and 85*29 = 2465 are Carmichael numbers.


MATHEMATICA

carmichaelQ[n_]:= Not[PrimeQ[n]] && Divisible[n1, CarmichaelLambda[n]];
numSol[n_] := Module[{m = 0}, ds = Divisors[n1]; Do[p = ds[[k]] + 1; If[! PrimeQ[p], Continue[]]; If[! carmichaelQ[p*n], Continue[]]; m++, {k, 1, Length[ds]  1}]; m]; numSolmax = 1; seq = {}; nums = {}; Do[m = numSol[n]; If[m > numSolmax, AppendTo[seq, n]; AppendTo[nums, m]; numSolmax = m], {n, 1, 10^8}]; seq


CROSSREFS

Cf. A002997.
Sequence in context: A039833 A250732 A080700 * A080200 A067705 A075213
Adjacent sequences: A292363 A292364 A292365 * A292367 A292368 A292369


KEYWORD

nonn,more


AUTHOR

Amiram Eldar, Sep 15 2017


STATUS

approved



