A306338 Carmichael numbers k such that phi(k) divides (k-1)*lambda(k).

561, 1105, 1729, 2465, 6601, 15841, 41041, 46657, 52633, 75361, 115921, 334153, 340561, 658801, 670033, 2455921, 2704801, 4903921, 5049001, 6049681, 6840001, 8355841, 9439201, 9582145, 9613297, 10402561, 11119105, 11205601, 11972017, 14469841, 15888313, 16778881

Offset: 1

Author

Amiram Eldar and Thomas Ordowski, Feb 08 2019

Keywords

• nonn

Comments

Carmichael numbers k such that A034380(k) divides k-1.

A proper subset of Carmichael numbers in A173703.

The number of terms below 10^k for k=1,2,...,18 is 0, 0, 1, 5, 10, 15, 25, 56, 101, 184, 310, 508, 814, 1265, 1964, 2990, 4486, 6704. Cf. A055553.

Composite numbers k such that lcm(lambda(k),phi(k)/lambda(k)) divides k-1.

Problem: are there infinitely many such numbers?

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to Carmichael numbers.

Crossrefs

Cf. A000010, A002322, A002997, A034380, A173703.

Programs

Mathematica

Select[Range[3, 100000, 2], !PrimeQ[#] && Divisible[#-1, c = CarmichaelLambda[#]] && Divisible[c*(#-1), EulerPhi[#]] &]