A066232 Numbers k such that phi(k) = phi(k-2) - phi(k-1).

195, 3531, 9339, 27231, 46795, 78183, 90195, 112995, 135015, 437185, 849405, 935221, 1078581, 1283601, 1986975, 2209585, 2341185, 2411175, 2689695, 2744145, 3619071, 3712545, 4738185, 5132985, 6596121, 7829031, 8184715, 12176109

Offset: 1

Author

Joseph L. Pe, Dec 18 2001

Keywords

• nonn

Comments

As in A065557, all terms listed here are odd. Problem: Prove that this holds in general.

Examples

			Phi(195) = 96 = 192-96 = phi(193)-phi(194).
		

Links

• Harry J. Smith and Jud McCranie, Table of n, a(n) for n = 1..289 (first 55 terms from Harry J. Smith)

Crossrefs

Cf. A065557, A066231, A067701, A197112, A220160.

Programs

Mathematica

Select[Range[3, 10^6], EulerPhi[ # ] == EulerPhi[ # - 2] - EulerPhi[ # - 1] &]

PARI

isok(k) = { k > 2 && eulerphi(k) == eulerphi(k - 2) - eulerphi(k - 1) } \\ Harry J. Smith, Feb 07 2010

Formula

a(n) = A220160(n) + 1 = A197112(n) + 2. - Andrew Howroyd, Dec 19 2024

Extensions

a(13)-a(28) from Harry J. Smith, Feb 07 2010