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 A007366 M4685 #114 Nov 17 2024 07:18:17
%S A007366 1,10,22,28,30,46,52,54,58,66,70,78,82,102,106,110,126,130,136,138,
%T A007366 148,150,166,172,178,190,196,198,210,222,226,228,238,250,262,268,270,
%U A007366 282,292,294,306,310,316,330,342,346,358,366,372,378,382,388,418,430,438
%N A007366 Numbers k such that phi(x) = k has exactly 2 solutions.
%C A007366 Contains {2*3^(6k+1): k >= 1} as a subsequence. This is the simplest proof for the infinity of these numbers (see Sierpiński, Exercise 12, p. 237). - _Franz Vrabec_, Aug 21 2021
%C A007366 The smaller of the solutions to phi(x) = a(n) is given by A271983(n). It is conjectured that the larger solution is 2*A271983(n); or equivalently, all terms in A271983 are odd. - _Jianing Song_, Nov 08 2022
%D A007366 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 A007366 Wacław Sierpiński, Elementary Theory of Numbers, Warszawa, 1964.
%D A007366 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A007366 Amiram Eldar, <a href="/A007366/b007366.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from T. D. Noe)
%H A007366 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 A007366 Max Alekseyev, <a href="https://oeis.org/wiki/User:Max_Alekseyev/gpscripts">PARI/GP Scripts for Miscellaneous Math Problems</a> (invphi.gp).
%H A007366 Robert G. Wilson v, <a href="/A007015/a007015.pdf">Letter to N. J. A. Sloane, Jul. 1992</a>.
%F A007366 #({phi^(-1)(a(n))}) = 2. - _Torlach Rush_, Dec 22 2017
%e A007366 10 = phi(11) = phi(22).
%p A007366 select(nops@numtheory:-invphi=2, [$1..1000]); # _Robert Israel_, Dec 20 2017
%t A007366 a = Table[ 0, {500} ]; Do[ p = EulerPhi[ n ]; If[ p < 501, a[ [ p ] ]++ ], {n, 1, 500} ]; Select[ Range[ 500 ], a[ [ # ] ] == 2 & ]
%t A007366 (* Second program: *)
%t A007366 With[{nn = 1325}, TakeWhile[Union@ Select[KeyValueMap[{#1, Length@ #2} &, PositionIndex@ Array[EulerPhi, nn]], Last@ # == 2 &][[All, 1]], # < nn/3 &] ] (* _Michael De Vlieger_, Dec 20 2017 *)
%o A007366 (PARI) is(k) = invphiNum(k) == 2 \\ _Amiram Eldar_, Nov 16 2024, using _Max Alekseyev_'s invphi.gp
%Y A007366 Cf. A000010, A001221, A023900, A271983.
%Y A007366 Number of solutions: A007617 (0), this sequence (2), A007367 (3), A060667 (4), A060668 (5), A060669 (6), A060670 (7), A060671 (8), A060672 (9), A060673 (10), A060674 (11), A060675 (12).
%K A007366 nonn
%O A007366 1,2
%A A007366 _N. J. A. Sloane_, _Mira Bernstein_, _Robert G. Wilson v_