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A173581 Numbers n such that tau(sigma(n)) = rad(n) 0

%I

%S 1,2,3,4,6,12,16,48,64,81,162,192,270,324,750,1029,1296,1512,2058,

%T 4096,4116,5184,12288,16464,65536,65856,196608,262144,331776,786432,

%U 2100000,4214784,5308416,21233664,67436544,269746176,1073741824,3221225472

%N Numbers n such that tau(sigma(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) sigma(n) is the sum of divisor of n (A000203).

%H C. K. Caldwell, <a href="http://primes.utm.edu/glossary/page.php?sort=Tau">The Prime Glossary, Number of divisors</a>

%H W. Sierpinski, <a href="http://matwbn.icm.edu.pl/ksiazki/mon/mon42/mon4204.pdf">Number Of Divisors And Their Sum</a>

%F n such that A062068(n)= A007947(n)

%e sigma(2) = 3, tau(3) = 2 and rad(2) = 2 sigma(65856) = 203200, tau(203200) = 42 and rad(65856) = 42

%p with(numtheory):for n from 1 to 10000000 do : t1:= ifactors(n)[2] : t2 :=mul(t1[i][1], i=1..nops(t1)):if tau(sigma(n)) = t2 then print (n): else fi: od :

%K nonn

%O 1,2

%A _Michel Lagneau_, Feb 22 2010

%E a(31)-a(38) from _Donovan Johnson_, Jan 14 2012

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Last modified January 29 14:23 EST 2020. Contains 331338 sequences. (Running on oeis4.)