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%I #20 Mar 16 2019 16:09:48
%S 1,3,4,5,8,14,16,17,18,21,22,26,28,32,33,35,36,38,39,44,45,46,50,52,
%T 54,55,56,57,58,63,64,65,69,72,74,75,76,82,87,88,91,92,94,95,100,104,
%U 106,108,111,112,115,116,117,118,119,123,128,133,135,141,144,145,146,148
%N Numbers k such that k and EulerPhi(k) have same number of prime factors, counted without multiplicity.
%H Reinhard Zumkeller, <a href="/A055742/b055742.txt">Table of n, a(n) for n = 1..10000</a>
%F A001221(A000010(n)) = A001221(n).
%e Known Fermat primes 3 and 5 are terms because their phi value is divisible only by 2. Several composites are also here, such as {50, 999, 1000} with prime factors (2,5), (3,37) and (2,5); their phi values, {20, 648, 400}, also have 2 prime factors: (2,5), (2,3), (2,5).
%t Select[Range[200],PrimeNu[#]==PrimeNu[EulerPhi[#]]&] (* _Harvey P. Dale_, Sep 12 2014 *)
%o (Haskell)
%o a055742 n = a055742_list !! (n-1)
%o a055742_list = [x | x <- [1..], a001221 x == a001221 (a000010 x)]
%o -- _Reinhard Zumkeller_, Apr 14 2015
%o (PARI) is(n)=my(f=factor(n)); #f~ == omega(eulerphi(f)) \\ _Charles R Greathouse IV_, Mar 01 2017
%Y Cf. A001221, A000010, A055744, A070418.
%K nonn
%O 1,2
%A _Labos Elemer_, Jul 11 2000
%E Definition clarified by _Harvey P. Dale_, Sep 12 2014
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