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Numbers k such that tau(tau(k)) = rad(k).
1

%I #15 May 10 2019 22:38:08

%S 1,2,4,16,27,64,72,96,108,288,432,486,648,768,972,1024,1536,1728,3456,

%T 4096,5832,6561,13122,17496,20736,24576,27648,39366,41472,65536,98304,

%U 104976,110592,147456,186624,256000,262144,314928,400000,419904,472392

%N Numbers k such that tau(tau(k)) = rad(k).

%C Tau = A000005 is the number of divisors of its argument. rad(n) = A007947(n) is the product of the primes dividing n.

%C Note that rad() is idempotent: rad(rad(n)) = rad(n). - _R. J. Mathar_, Nov 07 2011

%H Donovan Johnson, <a href="/A173746/b173746.txt">Table of n, a(n) for n = 1..496</a> (terms < 10^18)

%F {n : A010553(n) = A007947(n)}.

%e 288 is in the sequence because tau(288)= 18, tau(18)=6, rad(288)=6.

%p A010553 := proc(n)

%p numtheory[tau](numtheory[tau](n)) ;

%p end proc:

%p for n from 1 to 480000 do

%p if A010553(n) = A007947(n) then

%p printf("%d,",n) ;

%p end if;

%p end do: # _R. J. Mathar_, Nov 07 2011

%K nonn

%O 1,2

%A _Michel Lagneau_, Feb 23 2010

%E Example corrected and edited by _Michel Lagneau_, Apr 25 2010