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A161962 Odd numbers k such that phi(k) < phi(k+1). 8

%I

%S 105,165,315,525,585,735,1155,1365,1485,1575,1755,1785,1815,1995,2145,

%T 2205,2415,2475,2535,2805,2835,3003,3045,3315,3465,3675,3885,3927,

%U 4095,4125,4305,4455,4485,4515,4725,4785,4845,4935,5115,5145

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

%C 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.

%H G. C. Greubel, <a href="/A161962/b161962.txt">Table of n, a(n) for n = 1..5000</a>

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

%p 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

%t Select[Range[5500], OddQ[#] && EulerPhi[#] < EulerPhi[# + 1] &] (* _G. C. Greubel_, Feb 27 2019 *)

%o (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

%o (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

%o (PARI) for(n=1, 5500, if(Mod(n+1,2)==0 && eulerphi(n) < eulerphi(n+1), print1(n", "))) \\ _G. C. Greubel_, Feb 27 2019

%Y Cf. A000010, A161963.

%K easy,nonn

%O 1,1

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

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Last modified April 3 01:39 EDT 2020. Contains 333195 sequences. (Running on oeis4.)