A161963 Even numbers n for which phi(n) > phi(n+1).

314, 524, 734, 824, 944, 974, 1154, 1364, 1574, 1754, 1784, 1814, 1994, 2144, 2414, 2474, 2624, 2804, 3044, 3134, 3254, 3314, 3464, 3704, 3884, 4094, 4124, 4304, 4388, 4514, 4724, 4874, 4934, 5114, 5144, 5354, 5444, 5564, 5774, 5864

Offset: 1

Author

David Angell (angell(AT)maths.unsw.edu.au), Jun 22 2009

Keywords

• easy
• nonn

Comments

If n is even then for obvious reasons phi(n) will usually be less than or equal to phi(n+1). These are the first few exceptions.

Observation based upon calculation: More than 95% of the terms of this sequence have the final digit of 4 for n <= 10^7.. - Harvey P. Dale, Jul 24 2012

Examples

			314 is in the list because phi(314)=156 and phi(315)=144.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..5000 (terms 1..1000 from T. D. Noe)

Crossrefs

Cf. A001837, A161962.

Programs

Magma

[n: n in [1..6000] | (n mod 2 eq 0) and (EulerPhi(n) gt EulerPhi(n+1))]; // G. C. Greubel, Feb 27 2019

Mathematica

Select[2*Range[3000],EulerPhi[#]>EulerPhi[#+1]&] (* Harvey P. Dale, Jul 24 2012 *)

PARI

for(n=1, 6000, if(Mod(n,2)==0 && eulerphi(n) > eulerphi(n+1), print1(n", "))) \\ G. C. Greubel, Feb 27 2019

Sage

[n for n in (1..6000) if mod(n,2)==0 and euler_phi(n) > euler_phi(n+1)] # G. C. Greubel, Feb 27 2019

Formula

a(n) = 2 * A001837(n) (follows from the definition). - Chris Boyd, Mar 15 2014