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 A053099 #17 Nov 19 2024 01:02:27
%S A053099 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 A053099 87,92,97,99,104,106,111,118,123,127,132,136,137,144,148,155,159,163,
%U A053099 169,173,177,181,184,190,193,199,205,211,218,226,232,238,241,247,253
%N 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.
%C A053099 Analogous to A053048.
%H A053099 Amiram Eldar, <a href="/A053099/b053099.txt">Table of n, a(n) for n = 1..10000</a>
%F A053099 a(n) = log_2(A053098(n)). - _Amiram Eldar_, Nov 19 2024
%e A053099 For 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.
%t A053099 a[n_] := Max@ IntegerExponent[ FixedPointList[ EulerPhi, Times @@ Prime[ Range@ n]], 2]; Array[a, 60] (* _Giovanni Resta_, May 30 2018 *)
%o A053099 (PARI) a(n) = {my(p = prod(i=1, n, prime(i))); while(p >> valuation(p, 2) > 1, p = eulerphi(p)); valuation(p, 2);} \\ _Amiram Eldar_, Nov 19 2024
%Y A053099 Cf. A000010, A002110, A053048, A053098.
%K A053099 nonn
%O A053099 1,3
%A A053099 _Labos Elemer_, Feb 28 2000