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A301868 Numbers k such that phi(k, 2) = phi(k+1, 2), where phi(k, 2) = A002472(k).

%I A301868 #24 Mar 26 2023 02:21:12
%S A301868 1,2,9,34,50,153,274,321,2841,4610,7474,8254,10250,13430,22149,38961,
%T A301868 51981,86845,91310,198057,237325,367629,374541,394834,419169,489445,
%U A301868 513890,516350,519230,570230,717969,1308609,1523630,1557909,1753730,1935362,2109969,3005409
%N A301868 Numbers k such that phi(k, 2) = phi(k+1, 2), where phi(k, 2) = A002472(k).
%H A301868 Amiram Eldar, <a href="/A301868/b301868.txt">Table of n, a(n) for n = 1..200</a>
%H A301868 Henry L. Alder, <a href="http://www.jstor.org/stable/2308710">A Generalization of the Euler phi-Function</a>, The American Mathematical Monthly, Vol. 65, No. 9 (Nov., 1958), pp. 690-692.
%e A301868 phi(9, 2) = phi(10, 2) = 3, thus 9 is in the sequence.
%t A301868 seq = {}; a[n_] := If[Head[r = Reduce[GCD[x, n] == 1 && GCD[x + 2, n] == 1 && 1 <= x <= n, x, Integers]] === Or, Length[r], 1]; a0 = a[1]; Do[
%t A301868 a1 = a[k + 1]; If[a1 == a0, AppendTo[seq, k]]; a0 = a1, {k, 1, 1000}]; seq (* after _Jean-François Alcover_ at A002472 *)
%o A301868 (PARI) f(n) = sum(x=1, n, (gcd(n, x) == 1) && (gcd(n, x+2) == 1));
%o A301868 isok(n) = f(n) == f(n+1); \\ _Michel Marcus_, Apr 09 2018
%Y A301868 Cf. A002472.
%K A301868 nonn
%O A301868 1,2
%A A301868 _Amiram Eldar_, Mar 28 2018
%E A301868 a(20)-a(29) from _Robert Price_, May 18 2018
%E A301868 More terms from _Amiram Eldar_, Mar 26 2023