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Number k such that gcd(phi(k), k-1) = number of distinct prime factors of k.
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%I #15 Sep 18 2024 08:43:56

%S 2,4,8,15,16,32,35,39,51,55,63,64,70,75,87,95,99,111,115,119,123,128,

%T 130,135,143,147,154,155,159,171,183,187,203,207,215,219,235,238,256,

%U 267,275,279,280,287,291,295,299,303,310,319,322,323,327,335,339,351

%N Number k such that gcd(phi(k), k-1) = number of distinct prime factors of k.

%C Number of primes counted without multiplicity. - _Harvey P. Dale_, Jun 19 2020

%H Harvey P. Dale, <a href="/A039743/b039743.txt">Table of n, a(n) for n = 1..1000</a>

%e phi(15) = 8, gcd(8, 14) = 2, 15 = 3*5, 2 prime factors.

%t Select[Range[400],GCD[EulerPhi[#],#-1]==PrimeNu[#]&] (* _Harvey P. Dale_, Jun 19 2020 *)

%o (PARI) is(k) = k > 1 && gcd(eulerphi(k), k-1) == omega(k); \\ _Amiram Eldar_, Sep 18 2024

%Y Cf. A000010, A001221.

%K nonn,easy

%O 1,1

%A _Olivier GĂ©rard_

%E Definition clarified by _Harvey P. Dale_, Jun 19 2020