%I
%S 91,95,133,145,185,203,215,217,259,275,301,335,343,355,365,395,427,
%T 469,497,545,551,553,575,635,637,649,655,703,725,755,763,767,785,815,
%U 817,833,865,889,893,905,917,931,949,955,973,985,995,1007,1027,1057,1073
%N Weird totient numbers: totient abundant numbers (A286265) that are not pseudoperfect totient numbers (A288452).
%C Analogous to A006037 (weird numbers) as A082897 (perfect totient numbers) is analogous to A000396 (perfect numbers).
%e The set of iterated phi of 91 is {72, 24, 8, 4, 2, 1} and none of its subsets sums to 91.
%t pseudoPerfectTotQ[n_] := Module[{tots = Most[Rest[FixedPointList[EulerPhi@# &, n]]]}, MemberQ[Total /@ Subsets[tots, Length[tots]], n]];
%t totAbundantQ[n_] := Plus @@ FixedPointList[EulerPhi@# &, n] > 2*n + 1;
%t weirdTotient[n_] := totAbundantQ[n] && ! pseudoPerfectTotQ[n];
%t Select[Range[1100], weirdTotient]
%Y Cf. A000010, A000396, A006037, A092693, A082897, A286265.
%K nonn
%O 1,1
%A _Amiram Eldar_, Jun 09 2017
