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 A007367 M2163 #78 Nov 17 2024 07:18:28
%S A007367 2,44,56,92,104,116,140,164,204,212,260,296,332,344,356,380,392,444,
%T A007367 452,476,524,536,564,584,588,620,632,684,692,716,744,764,776,836,860,
%U A007367 884,932,956,980,1004,1016,1112,1124,1136,1172,1196,1284,1292,1304
%N A007367 Numbers k such that phi(x) = k has exactly 3 solutions.
%C A007367 From _Torlach Rush_, Jul 23 2018: (Start)
%C A007367 For known terms:
%C A007367 - The greatest common divisor of the three solutions is the distance of the middle solution from the least solution and is half the distance of the middle solution to the largest solution.
%C A007367 - If the number of distinct prime factors of k equals the number of solutions of k = phi(x), then the greatest common divisor of the solutions is the least solution divided by the number of solutions.
%C A007367 - Except for a(1), if the largest prime factor is the same for all solutions and is equal to the greatest common divisor of all solutions then the distance from a(n) to the least solution is gcd({k: phi(k) = a(n)}) + 2. (End)
%C A007367 By Ford's theorem on Euler totient function, this sequence is infinite. - _Jianing Song_, Jul 18 2018
%D A007367 M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 840.
%D A007367 Jean-Marie De Koninck, Ces nombres qui nous fascinent, Entry 44, p. 17, Ellipses, Paris, 2008.
%D A007367 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A007367 Amiram Eldar, <a href="/A007367/b007367.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from T. D. Noe)
%H A007367 M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
%H A007367 Max Alekseyev, <a href="https://oeis.org/wiki/User:Max_Alekseyev/gpscripts">PARI/GP Scripts for Miscellaneous Math Problems</a> (invphi.gp).
%H A007367 Wikipedia, <a href="https://en.wikipedia.org/wiki/Euler%27s_totient_function#Ford's_theorem">Ford's theorem</a>.
%H A007367 Robert G. Wilson v, <a href="/A007015/a007015.pdf">Letter to N. J. A. Sloane, Jul. 1992</a>.
%e A007367 phi(69) = phi(92) = phi(138) = 44, so 44 is a term.
%t A007367 a = Table[ 0, {1500} ]; Do[ p = EulerPhi[ n ]; If[ p < 1501, a[ [ p ] ]++ ], {n, 1, 1500} ]; Select[ Range[ 1500 ], a[ [ # ] ] == 3 & ]
%t A007367 Take[Select[Tally[EulerPhi[Range[50000]]],#[[2]]==3&][[All,1]],50]//Sort (* _Harvey P. Dale_, Apr 02 2018 *)
%o A007367 (Haskell)
%o A007367 a007367 n = a007367_list !! (n-1)
%o A007367 a007367_list = map fst $
%o A007367 filter ((== 3) . snd) $ zip a002202_list a058277_list
%o A007367 -- _Reinhard Zumkeller_, Nov 25 2015
%o A007367 (PARI) is(k) = invphiNum(k) == 3 \\ _Amiram Eldar_, Nov 17 2024, using _Max Alekseyev_'s invphi.gp
%Y A007367 Cf. A000010, A002202, A058277, A085713.
%Y A007367 Number of solutions: A007617 (0), A007366 (2), this sequence (3), A060667 (4), A060668 (5), A060669 (6), A060670 (7), A060671 (8), A060672 (9), A060673 (10), A060674 (11), A060675 (12).
%K A007367 nonn
%O A007367 1,1
%A A007367 _N. J. A. Sloane_, _Mira Bernstein_, _Robert G. Wilson v_