A277366 Composite numbers k such that phi(k)*lambda(k) divides (k-1)^2, where phi(k) = A000010(k) and lambda(k) = A002322(k).

1729, 670033, 6840001, 83099521, 193708801, 321197185, 367804801, 484662529, 1752710401, 2320690177, 5064928705, 12820178449, 32220147601, 257124585601, 270177600001, 301036080385, 7043394657601, 13237329899521, 14276860416001, 85661522006401, 119377939968001

Offset: 1

Author

Thomas Ordowski, Oct 11 2016

Keywords

• nonn

Comments

Are there infinitely many such numbers?

Such k must be a Carmichael number since phi(k)*lambda(k) = m*lambda(k)^2 for some integer m. - Nathan McNew, Oct 11 2016

Links

• Amiram Eldar, Table of n, a(n) for n = 1..115 (terms below 10^22, calculated using data from Claude Goutier)
• Claude Goutier, Compressed text file carm10e22.gz containing all the Carmichael numbers up to 10^22.
• Index entries for sequences related to Carmichael numbers.

Crossrefs

Subsequence of A002997 and of A173703.

Cf. A000010, A002322, A002997, A173703.

Programs

Mathematica

Select[Range[10^8], CompositeQ[#] && Divisible[(# - 1)^2, EulerPhi[#] * CarmichaelLambda[#]] &] (* Amiram Eldar, Feb 02 2019 *)

PARI

lista(nn) = forcomposite(n=4, nn, if (((n-1)^2 % (eulerphi(n)*lcm(znstar(n)[2]))) == 0, print1(n, ", "));); \\ Michel Marcus, Oct 11 2016

PARI

is(n,f=factor(n))=(n-1)^2%(eulerphi(f)*lcm(znstar(f)[2])) == 0 && !isprime(n) && n>1 \\ Charles R Greathouse IV, Oct 11 2016

Extensions

a(2)-a(3) from Michel Marcus, Oct 11 2016

a(4)-a(8) from Charles R Greathouse IV, Oct 11 2016

a(9)-a(13) from David A. Corneth, Oct 11 2016

More terms from Amiram Eldar, Feb 02 2019