A049116 - OEIS

%I #9 Jul 19 2019 14:24:11

%S 1,2,2,4,4,2,2,8,2,4,4,4,4,2,8,16,16,2,2,8,4,4,4,8,8,4,2,4,4,8,8,32,8,

%T 16,8,4,4,2,8,16,16,4,4,8,8,4,4,16,4,8,32,8,8,2,16,8,4,4,4,16,16,8,4,

%U 64,16,8,8,32,8,8,8,8,8,4,16,4,16,8,8,32,2,16,16,8,64,4,8,16,16,8,8,8

%N Repeatedly apply Euler phi to n; a(n) = highest power of 2 that is seen.

%H Amiram Eldar, <a href="/A049116/b049116.txt">Table of n, a(n) for n = 1..10000</a>

%e If n is a power of 2, then it is of largest exponent. If n=2400, then its phi-sequence is {2400,640,256,128,64,32,16,8,4,2,1}. The value of first power of 2 is 256. Thus a(2400)=256.

%t Table[SelectFirst[NestWhileList[EulerPhi[#]&,n,#>1&],IntegerQ[Log[2,#]]&],{n,120}] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Mar 23 2019 *)

%Y Cf. A000010.

%K nonn

%O 1,2

%A _Labos Elemer_