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Numbers k such that the number of primes <= k is phi(phi(k)).
1

%I #19 Aug 19 2019 04:01:57

%S 2,37,55,91,95,136,178,226,507,723,1166,1168,1284,1323,2658,3082,7564,

%T 8166,11578,12014,12018,12026,15340,40220,50544,55490,56810,69732,

%U 89210,100114,100126,111306,131532,226716,226722,232938,519312,683240,849534

%N Numbers k such that the number of primes <= k is phi(phi(k)).

%H Harry J. Smith, <a href="/A063999/b063999.txt">Table of n, a(n) for n = 1..44</a>

%e 37 belongs to the sequence because number of primes <= 37 is equal to 12 (counting 2,3,5,7,11,13,17,19,23,29,31,37), while phi(37)=36 (counting 1,2,...,36) and phi(36)=12 (counting 1,5,7,11,13,17,19,23,25,29,31,35).

%p with(numtheory): p:=proc(n) if pi(n)=phi(phi(n)) then n else fi end: seq(p(n), n=1..900000); # _Emeric Deutsch_, Feb 24 2005

%o (PARI) pi(n) = s=0; for(x=1,n, if(isprime(x),s++)); s; for(n=1,10^6, if(pi(n)==eulerphi(eulerphi(n)),print(n)))

%o (PARI) { default(primelimit, 2500000); n=0; for (m=1, 10^9, if (primepi(m)==eulerphi(eulerphi(m)), write("b063999.txt", n++, " ", m); if (n==44, break)) ) } \\ _Harry J. Smith_, Sep 05 2009

%Y Cf. A000720, A010554.

%K nonn

%O 1,1

%A _Jason Earls_, Sep 06 2001

%E More terms from _Emeric Deutsch_, Feb 24 2005