A161962 Odd numbers k such that phi(k) < phi(k+1).

105, 165, 315, 525, 585, 735, 1155, 1365, 1485, 1575, 1755, 1785, 1815, 1995, 2145, 2205, 2415, 2475, 2535, 2805, 2835, 3003, 3045, 3315, 3465, 3675, 3885, 3927, 4095, 4125, 4305, 4455, 4485, 4515, 4725, 4785, 4845, 4935, 5115, 5145

Offset: 1

Author

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

Keywords

• easy
• nonn

Comments

If k is even then for obvious reasons phi(k) will usually be less than phi(k+1). So it is more interesting to see when this occurs for odd k.

Examples

			105 is in the sequence since phi(105)=48 and phi(106)=52.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A000010, A001836, A161963.

Programs

Magma

[n: n in [1..5500] | ((n+1) mod 2 eq 0) and (EulerPhi(n) lt EulerPhi(n+1))]; // G. C. Greubel, Feb 27 2019

Maple

with(numtheory): a := proc (n) if `mod`(n, 2) = 1 and phi(n) < phi(n+1) then n else end if end proc: seq(a(n), n = 1 .. 6000); # Emeric Deutsch, Jul 11 2009

Mathematica

Select[Range[5500], OddQ[#] && EulerPhi[#] < EulerPhi[# + 1] &] (* G. C. Greubel, Feb 27 2019 *)
2#-1&/@Flatten[Position[Partition[EulerPhi[Range[5500]],2],?(#[[1]]<#[[2]]&),1,Heads-> False]] (* _Harvey P. Dale, Nov 25 2022 *)

PARI

for(n=1, 5500, if(Mod(n+1,2)==0 && eulerphi(n) < eulerphi(n+1), print1(n", "))) \\ G. C. Greubel, Feb 27 2019

Sage

[n for n in (1..5500) if mod(n+1,2)==0 and euler_phi(n) < euler_phi(n+1)] # G. C. Greubel, Feb 27 2019

Formula

a(n) = 2*A001836(n) - 1. - Jon Maiga / Georg Fischer, Jun 23 2021