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 A066669 #20 Feb 11 2025 01:30:24 %S A066669 7,9,11,13,14,18,21,22,23,25,26,28,29,33,35,36,39,41,42,44,45,46,47, %T A066669 50,52,53,55,56,58,59,65,66,69,70,72,75,78,82,83,84,87,88,89,90,92,94, %U A066669 97,100,104,105,106,107,110,112,113,115,116,118,119,123,130,132,137,138 %N A066669 Numbers m such that phi(m) = 2^k*prime for some k >= 0. %C A066669 Sequence is infinite, since 2n is in the sequence if and only if n is in the sequence. What is its density? - _Charles R Greathouse IV_, Feb 21 2013 %C A066669 Products of powers of 2, distinct terms (at least one) of A074781, and possibly (if all the factors from A074781 are Fermat primes, A019434) an additional Fermat prime (i.e., it can be divisible by a square of one Fermat prime, A330828). - _Amiram Eldar_, Feb 11 2025 %H A066669 Charles R Greathouse IV, <a href="/A066669/b066669.txt">Table of n, a(n) for n = 1..10000</a> %e A066669 7 is a term because phi(7) = 6 divided by 2 is 3, a prime. %e A066669 21 is a term because phi(21) = 12 divided by 4 is 3, a prime. %e A066669 15 is not a term because phi(15) = 8 divided by 8 is 1, not a prime. %t A066669 Select[Range@ 138, PrimeQ@ Last@ Most@ NestWhileList[#/2 &, EulerPhi@ #, IntegerQ@ # &] &] (* _Michael De Vlieger_, Mar 18 2017 *) %o A066669 (PARI) is(n)=n=eulerphi(n);isprime(n>>valuation(n,2)) \\ _Charles R Greathouse IV_, Feb 21 2013 %Y A066669 Cf. A000010, A066670, A066671, A066672, A066673, A065966. %Y A066669 Cf. A019434, A058500, A074781, A330828. %K A066669 nonn %O A066669 1,1 %A A066669 _Labos Elemer_, Dec 18 2001