

A173581


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


0



1, 2, 3, 4, 6, 12, 16, 48, 64, 81, 162, 192, 270, 324, 750, 1029, 1296, 1512, 2058, 4096, 4116, 5184, 12288, 16464, 65536, 65856, 196608, 262144, 331776, 786432, 2100000, 4214784, 5308416, 21233664, 67436544, 269746176, 1073741824, 3221225472
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OFFSET

1,2


COMMENTS

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).


LINKS

Table of n, a(n) for n=1..38.
C. K. Caldwell, The Prime Glossary, Number of divisors
W. Sierpinski, Number Of Divisors And Their Sum


FORMULA

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


EXAMPLE

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


MAPLE

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 :


CROSSREFS

Sequence in context: A002809 A015904 A015888 * A075122 A018333 A044954
Adjacent sequences: A173578 A173579 A173580 * A173582 A173583 A173584


KEYWORD

nonn


AUTHOR

Michel Lagneau, Feb 22 2010


EXTENSIONS

a(31)a(38) from Donovan Johnson, Jan 14 2012


STATUS

approved



