A039767 Numbers k such that gcd(phi(k), k-1) = number of distinct prime factors of (k-1).

4, 6, 8, 10, 12, 14, 15, 18, 20, 24, 26, 27, 30, 32, 35, 38, 39, 42, 44, 48, 50, 51, 54, 55, 60, 62, 63, 68, 72, 74, 75, 80, 81, 82, 84, 87, 90, 95, 98, 99, 102, 104, 108, 110, 114, 119, 122, 123, 126, 128, 132, 135, 138, 140, 143, 147, 150, 152, 158, 159, 164, 168

Offset: 1

Author

Olivier Gérard

Keywords

• nonn
• easy

Comments

If k = p+1 where p is an odd prime, then k is a term. - Amiram Eldar, Sep 16 2024

Examples

			phi(15) = 8, gcd(8, 14) = 2, 14 = 2*7, 2 prime factors.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000010, A001221, A049559, A209211.

Programs

Mathematica

q[k_] := GCD[EulerPhi[k], k-1] == PrimeNu[k-1]; Select[Range[200], q] (* Amiram Eldar, Sep 16 2024 *)

PARI

is(k) = k > 1 && gcd(eulerphi(k), k-1) == omega(k-1); \\ Amiram Eldar, Sep 16 2024