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%I #11 Apr 02 2023 05:56:11
%S 3,7,14,15,31,54,62,63,127,154,174,182,186,234,246,254,255,294,308,
%T 318,322,364,406,414,496,510,511,516,534,558,574,594,644,666,678,762,
%U 804,806,812,846,870,948,1022,1023,1026,1036,1074,1098,1146,1148,1164,1204,1246
%N Numbers k with a single solution x to the equation uphi(x) = k, where uphi is the unitary totient function (A047994).
%C Numbers k such that A361967(k) = 1.
%C According to Carmichael's totient function conjecture, there are no numbers with a single solution x to the corresponding equation phi(x) = k, with Euler's totient function (A000010).
%C A000225(m) = 2^m - 1 is a term for all m >= 2. These are the only odd terms.
%H Amiram Eldar, <a href="/A361969/b361969.txt">Table of n, a(n) for n = 1..10000</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Carmichael%27s_totient_function_conjecture">Carmichael's totient function conjecture</a>.
%t Select[Range[1250], Length[invUPhi[#]] == 1 &] (* using the function invUPhi from A361966 *)
%Y Cf. A000010, A000225, A047994, A135347, A361966, A361967, A361968, A361970, A361971.
%K nonn
%O 1,1
%A _Amiram Eldar_, Apr 01 2023