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Select[Range[800000], Divisible[DivisorSigma[11, #]-EulerPhi[#]^11, #]&] (* Harvey P. Dale, Apr 15 2018 *)
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sigma_11(n) is the sum of the 11-th 11th powers of the divisors of n (A013959).
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Do[If[Mod[DivisorSigma[11, n]-EulerPhi[n]^11, n]==0, Print[n]], {n, 1, 10^5}]
Cf. A000010.
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Definition corrected by and more terms from Michel Marcus, Mar 02 2014