This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A053097 #18 Aug 17 2024 09:01:48
%S A053097 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 A053097 82,88,93,98,100,105,107,112,119,124,128,133,137,138,145,149,156,160,
%U A053097 164,170,174,178,182,185,191,194,200,206,212,219,227,233,239,242,248,254
%N A053097 a(n) is the number of powers of 2 among the iterates of the Euler phi function when it is iterated with initial value A002110(n), the n-th primorial number.
%H A053097 Amiram Eldar, <a href="/A053097/b053097.txt">Table of n, a(n) for n = 1..10000</a>
%e A053097 For n=8, A002110(8) = 9699690 and 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 and it has 15 terms that are powers of 2. Thus a(8) = 15.
%t A053097 a[n_] := 1 + Max@ IntegerExponent[ FixedPointList[ EulerPhi, Times @@ Prime[Range[n]]], 2]; Array[a, 60] (* _Giovanni Resta_, May 30 2018 *)
%o A053097 (PARI) ispow2(n) = n >> valuation(n, 2) == 1;
%o A053097 a(n) = {my(p = vecprod(primes(n))); while(!ispow2(p), p = eulerphi(p)); valuation(p, 2) + 1;} \\ _Amiram Eldar_, Aug 17 2024
%Y A053097 Analogous to A053035, A053045.
%Y A053097 Cf. A000010, A002110.
%K A053097 nonn
%O A053097 1,1
%A A053097 _Labos Elemer_, Feb 28 2000