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Numbers k >= 1 such that k * phi(k) / (k + phi(k)) is an integer, where phi(k) = A000010(k).
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%I #8 Dec 31 2022 15:17:11

%S 12,24,36,48,72,96,108,126,144,176,192,216,252,288,324,352,378,384,

%T 432,504,576,648,704,756,768,864,882,972,1008,1134,1152,1296,1408,

%U 1512,1536,1728,1764,1936,1944,2016,2268,2304,2592,2646,2752,2816,2916

%N Numbers k >= 1 such that k * phi(k) / (k + phi(k)) is an integer, where phi(k) = A000010(k).

%C For k >= 12, A003586 is a subsequence.

%e k = 12 : 12 * phi(12) / (12 + phi(12)) = 12 * 4 / (12 + 4) = 3, thus 12 is a term.

%t Select[Range[3000], Divisible[#*(phi = EulerPhi[#]), # + phi] &] (* _Amiram Eldar_, Dec 31 2022 *)

%Y Cf. A000010, A003586, A033845.

%K nonn

%O 1,1

%A _Ctibor O. Zizka_, Dec 31 2022