A297361 Numbers k such that (3^lambda(k) - 1)/k is prime, where lambda(k) is the Carmichael lambda function (A002322).

4, 16, 40, 56, 160, 7280

Offset

1,1

Comments

The corresponding primes are 2, 5, 2, 13, 41, 73.

a(7) > 2*10^6. - Michael S. Branicky, Jan 06 2026

Links

Table of n, a(n) for n=1..6.

Example

4 is in the sequence since lambda(4) = 2 and (3^2 - 1)/4 = 2 is prime.

Mathematica

aQ[n_] := PrimeQ[(3^CarmichaelLambda[n]-1)/n]; a={}; Do[If[aQ[k], AppendTo[a, k]], {k, 1, 10000}]; a
Select[Range[2, 7300], PrimeQ[(3^CarmichaelLambda[#]-1)/#]&] (* Harvey P. Dale, Jan 02 2026 *)

Prog

(PARI) isok(n) = (denominator(p=(3^lcm(znstar(n)[2])-1)/n)==1) && isprime(p); \\ Michel Marcus, Dec 29 2017

Crossrefs

Cf. A002322.

Sequence in context: A121318 A152133 A371345 * A210440 A329892 A220499

Adjacent sequences: A297358 A297359 A297360 * A297362 A297363 A297364

Keyword

nonn,more

Author

Amiram Eldar, Dec 29 2017

Status

approved