A053099 - OEIS

A053099

When the Euler phi function is iterated with initial value A002110(n) = n-th primorial, a(n) = exponent of largest power of 2 arising in the iteration.

%I #10 May 30 2018 03:30:43

%S 1,1,3,4,7,9,13,14,18,21,24,26,31,33,38,42,46,50,54,58,61,64,70,76,81,

%T 87,92,97,99,104,106,111,118,123,127,132,136,137,144,148,155,159,163,

%U 169,173,177,181,184,190,193,199,205,211,218,226,232,238,241,247,253

%N When the Euler phi function is iterated with initial value A002110(n) = n-th primorial, a(n) = exponent of largest power of 2 arising in the iteration.

%C Analogous to A053048.

%e n=6, A002110(6)=30030; the corresponding iteration chain is {30030, 5760, 1536, 512, 256, 128, 64, 32, 16, 8, 4, 2, 1}. The first power of 2 is the 4th item after 3 iterations. It is 512, therefore a(6) = log_2(512) = 9 and a(6) + 1 = 10 iterations is needed to reach the stationary value = 1. a(6)=512.

%t a[n_] := Max@ IntegerExponent[ FixedPointList[ EulerPhi, Times @@ Prime[ Range@ n]], 2]; Array[a, 60] (* _Giovanni Resta_, May 30 2018 *)

%Y Cf. A000010, A002110.

%K nonn

%O 1,3

%A _Labos Elemer_, Feb 28 2000