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%I #10 May 30 2018 03:33:55
%S 2,2,4,5,8,10,14,15,19,22,25,27,32,34,39,43,47,51,55,59,62,65,71,77,
%T 82,88,93,98,100,105,107,112,119,124,128,133,137,138,145,149,156,160,
%U 164,170,174,178,182,185,191,194,200,206,212,219,227,233,239,242,248,254
%N When the Euler phi function is iterated with initial value A002110(n) = primorial, a(n) = number of powers of 2 among iterates.
%e n=8, A002110(8)=9699690; the corresponding iteration chain is {9699690, 1658880, 442368, 147456, 49152, 16384, 8192, 4096, 2048, 1024, 512, 256, 128, 64, 32, 16, 8, 4, 2, 1}. Its length is 20 of which 15 terms are powers of 2: a(8)=15. Its length is 17, so the required number of iterations is a(7)=16.
%t a[n_] := 1 + Max@ IntegerExponent[ FixedPointList[ EulerPhi, Times @@ Prime[Range[n]]], 2]; Array[a, 60] (* _Giovanni Resta_, May 30 2018 *)
%Y Analogous to A053035, A053045.
%Y Cf. A000010, A002110.
%K nonn
%O 1,1
%A _Labos Elemer_, Feb 28 2000
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