A284406 Odd numbers k such that lambda(k) < phi(k) and gcd(lambda(k), k-1) = gcd(phi(k), k-1).

15, 35, 39, 45, 51, 55, 63, 75, 85, 87, 95, 99, 111, 115, 117, 119, 123, 135, 143, 147, 153, 155, 159, 165, 171, 175, 183, 187, 195, 203, 205, 207, 215, 219, 221, 231, 235, 245, 247, 255, 259, 261, 267, 275, 279, 285, 287, 291, 295, 299, 303, 315, 319, 323, 325, 327, 333, 335, 339, 351

Offset: 1

Author

Thomas Ordowski and Altug Alkan, Mar 26 2017

Keywords

• nonn

Comments

If odd n is in A033949 and n-1 is squarefree, then n is in the sequence.

The set of such numbers has a positive natural density.

The density is 1/2. Almost all odd numbers have this property.

The number of terms below 10^k for k = 1, 2, ... are 0, 12, 204, 2507, 27801, 296583, 3102205, 32054920, 328714616, 3353406273, .... Apparently the asymptotic density of this sequence is less than 1/2. - Amiram Eldar, Jul 14 2020

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..439 from Indranil Ghosh)

Crossrefs

Subsequence of A257591.

A264012 is a subsequence.

Cf. A000010, A002322, A280262.

Programs

Mathematica

Select[Range[1, 351, 2], Function[k, And[#1 < #2, GCD[#1, k - 1] == GCD[#2, k - 1]] & @@ {CarmichaelLambda@ k, EulerPhi@ k}]] (* Michael De Vlieger, Mar 26 2017 *)