Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #20 Jul 18 2024 09:18:18
%S 2,2,2,4,2,2,4,2,2,4,4,4,4,4,8,4,8,8,4,4,8,2,2,4,8,4,8,8,4,2,16,4,4,8,
%T 8,8,8,8,2,8,8,8,8,8,4,2,32,8,16,16,4,2,8,16,16,8,8,2,32,16,16,8,8,4,
%U 16,4,16,16,4,8,32,16,8,16,16,2,2,16,4,8,16,4,8,2,16,8,32,4,64,32,32
%N a(n) is the largest power of 2 that divides phi(A066669(n)).
%H Michael De Vlieger, <a href="/A066671/b066671.txt">Table of n, a(n) for n = 1..10000</a>
%F From _Amiram Eldar_, Jul 18 2024:
%F a(n) = A069177(A066669(n)).
%F a(n) = 2^A066672(n). (End)
%e The first, 4th and 15th terms in A066669 are 7, 13 and 35; phi(7) = 2*3, phi(13) = 4*3, phi(35) = 24 = 8*3; the largest powers of 2 are 2, 4 and 8; so a(1) = 2, a(4) = 4, a(15) = 8.
%t Select[Array[{#1/#2, #2} & @@ {#, 2^IntegerExponent[#, 2]} &@ EulerPhi@ # &, 200], PrimeQ@ First@ # &][[All, -1]] (* _Michael De Vlieger_, Dec 08 2018 *)
%o (PARI) lista(nn) = {for (n=1, nn, en=eulerphi(n); if (isprime(p=en>>valuation(en, 2)), print1(en/p, ", ")););} \\ _Michel Marcus_, Jan 03 2017
%Y Cf. A000010, A065966, A066669, A066670, A066672, A066673, A069177.
%K nonn
%O 1,1
%A _Labos Elemer_, Dec 18 2001
%E Name corrected by _Amiram Eldar_, Jul 18 2024