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%I #7 Oct 24 2017 18:09:06
%S 1,2,3,6,20,28,45,75,90,147,150,169,176,189,208,252,294,336,338,378,
%T 480,608,792,875,1400,1444,1521,1715,1750,1960,2808,2904,3042,3159,
%U 3430,3744,4056,4624,6318,6591,6859,8448,11016,13182,13718,14700,16900
%N Numbers n such that tau(phi(n))= phi(rad(n))
%C Here rad(n) is the product of the primes dividing n (A007947), tau(n) is the number of divisors of n (A000005), phi(n): Euler totient function (A000010)
%D M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 840.
%H Harvey P. Dale, <a href="/A173744/b173744.txt">Table of n, a(n) for n = 1..300</a>
%H W. Sierpinski, <a href="http://matwbn.icm.edu.pl/ksiazki/mon/mon42/mon4204.pdf">Number Of Divisors And Their Sum</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Euler's_phi_function">Euler's totient function</a>
%F Numbers n such that A000005(A000010)(n) = A000010(A007947)(n)
%e for n=3,phi(3) = 2, tau(2)=2, rad(3)=3 and phi(3) = 2 for n=18900,phi(18900) =4320,tau(4320)= 48, rad(18900)=210, and phi(210) = 48
%p with(numtheory):for n from 1 to 20000 do: t1:= ifactors(n)[2] : t2 :=mul(t1[i][1], i=1..nops(t1)): if tau(phi(n))= phi(t2)then print (n): else fi: od :
%t Select[Range[17000],DivisorSigma[0,EulerPhi[#]]==EulerPhi[Times @@ FactorInteger[ #][[All,1]]]&] (* _Harvey P. Dale_, Oct 24 2017 *)
%K nonn
%O 1,2
%A _Michel Lagneau_, Feb 23 2010; corrected Feb 27 2010
%E Corrected by _Harvey P. Dale_, Oct 24 2017