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%I #11 Jul 12 2019 01:30:48
%S 1,4,8,32,36,192,288,768,972,1458,5120,13122,326592,19531250,22588608,
%T 46137344,171532242
%N Numbers n such that phi(tau(n))= rad(n)
%C 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)
%C a(18) > 10^10. - Donovan Johnson, Jul 27 2011
%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 P. A. MacMahon, <a href="https://doi.org/10.1112/plms/s2-19.1.75">Divisors of numbers and their continuations in the theory of partitions</a>, Proc. London Math. Soc., 19 (1919), 75-113.
%H W. Sierpinski, <a href="http://matwbn.icm.edu.pl/ksiazki/mon/mon42/mon4204.pdf">Number Of Divisors And Their Sum</a>, Elementary theory of numbers, Warszawa, 1964.
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Euler's_phi_function">Euler's totient function</a>
%F n such that A163109(n)= A007947(n)
%e tau(8) = 4, phi(4)=2 and rad(8)=2 tau(13122) = 18, phi(18)=6 and rad(13122)=6
%p with(numtheory):for n from 1 to 1000000 do :t1:= ifactors(n)[2] : t2 :=mul(t1[i][1], i=1..nops(t1)): if phi(tau(n)) = t2 then print (n): else fi : od :
%Y Cf. A173320, A062069, A001414, A001222.
%K nonn
%O 1,2
%A _Michel Lagneau_, Feb 22 2010
%E a(14)-a(17) from _Donovan Johnson_, Jul 27 2011
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