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Numbers n such that phi(n) = pi(n) + 2.
5

%I #15 Sep 08 2022 08:45:06

%S 7,9,15,16,22,54,66,120,210

%N Numbers n such that phi(n) = pi(n) + 2.

%F Solutions to A000010(x)=A000720(x)+k, where k=+2; finite for any fixed value of k.

%e 8 primes below 22 = {2,3,5,7,11,13,17,19}; 10 terms in RRS[22]={1,3,5,7,9,13,15,17,19,21}, so 22 is here.

%p with(numtheory): A073457:=n->`if`(phi(n) = pi(n) + 2, n, NULL): seq(A073457(n), n=1..210); # _Wesley Ivan Hurt_, May 12 2015

%t Do[s=EulerPhi[n]-PrimePi[n]; If[Equal[s, 2], Print[n]], {n, 10000}]

%o (Magma) [n: n in [2..1000] | EulerPhi(n) eq #PrimesUpTo(n)+2]; // _Vincenzo Librandi_, May 10 2015

%Y Cf. A037228, A037171, A000010, A000720, A073455, A072456.

%K fini,full,nonn

%O 1,1

%A _Labos Elemer_, Aug 02 2002