A063999 Numbers k such that the number of primes <= k is phi(phi(k)).

2, 37, 55, 91, 95, 136, 178, 226, 507, 723, 1166, 1168, 1284, 1323, 2658, 3082, 7564, 8166, 11578, 12014, 12018, 12026, 15340, 40220, 50544, 55490, 56810, 69732, 89210, 100114, 100126, 111306, 131532, 226716, 226722, 232938, 519312, 683240, 849534

Offset: 1

Author

Jason Earls, Sep 06 2001

Keywords

• nonn

Examples

			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).
		

Links

• Harry J. Smith, Table of n, a(n) for n = 1..44

Crossrefs

Cf. A000720, A010554.

Programs

Maple

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

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)))

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

Extensions

More terms from Emeric Deutsch, Feb 24 2005