A173746 Numbers k such that tau(tau(k)) = rad(k).

1, 2, 4, 16, 27, 64, 72, 96, 108, 288, 432, 486, 648, 768, 972, 1024, 1536, 1728, 3456, 4096, 5832, 6561, 13122, 17496, 20736, 24576, 27648, 39366, 41472, 65536, 98304, 104976, 110592, 147456, 186624, 256000, 262144, 314928, 400000, 419904, 472392

Offset: 1

Author

Michel Lagneau, Feb 23 2010

Keywords

• nonn

Comments

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

Note that rad() is idempotent: rad(rad(n)) = rad(n). - R. J. Mathar, Nov 07 2011

Examples

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

Links

• Donovan Johnson, Table of n, a(n) for n = 1..496 (terms < 10^18)

Programs

Maple

A010553 := proc(n)
        numtheory[tau](numtheory[tau](n)) ;
end proc:
for n from 1 to 480000 do
        if A010553(n) = A007947(n) then
                printf("%d,",n) ;
        end if;
end do: # R. J. Mathar, Nov 07 2011

Formula

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

Extensions

Example corrected and edited by Michel Lagneau, Apr 25 2010