A065572 Composite numbers k such that phi(k) = phi(k-1) + phi(k-2).

1037, 1541, 6527, 9179, 55387, 61133, 72581, 110177, 152651, 179297, 244967, 299651, 603461, 619697, 1876727, 2841917, 3058211, 3971321, 4110653, 4316441, 4397317, 6008861, 10076627, 10667801, 10835441, 11561597, 24571871, 36521777, 45981377

Offset: 1

Author

Len Smiley and Robert G. Wilson v, Nov 30 2001

Keywords

• nonn

Comments

619697 = 13*73*653 is the smallest solution not of the form p or p*q for distinct primes p and q.

218688017 is the first term that has four prime factors and 32617225577 is the first term with five prime factors. 72340252337 and 179115011177 are the first two that are not squarefree. There are 175 terms less than 5*10^11. - Jud McCranie, Feb 20 2012

Links

• Harry J. Smith and Jud McCranie, Table of n, a(n) for n = 1..175 (first 50 terms from Harry J. Smith)

Crossrefs

Cf. A065557 (includes prime solutions).

Programs

Mathematica

Select[ Range[3, 10^7], !PrimeQ[ # ] && EulerPhi[ # ] == EulerPhi[ # - 1] + EulerPhi[ # - 2] & ]

PARI

{ n=0; e1=eulerphi(2); e2=eulerphi(1); for (m=3, 10^9, e=eulerphi(m); if (!isprime(m) && e==e2 + e1, write("b065572.txt", n++, " ", m); if (n==100, return)); e2=e1; e1=e ) } \\ Harry J. Smith, Oct 23 2009

Extensions

More terms from Jud McCranie, Feb 21 2012