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

1,1

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)

Mathematica

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

Prog

(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

Crossrefs

Cf. A065557 (includes prime solutions).

Sequence in context: A184210 A163559 A159052 * A251876 A251869 A251868

Adjacent sequences: A065569 A065570 A065571 * A065573 A065574 A065575

Keyword

nonn

Author

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

Extensions

More terms from Jud McCranie, Feb 21 2012

Status

approved