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A173581
Numbers k such that tau(sigma(k)) = rad(k).
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
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), and sigma(n) is the sum of divisor of n (A000203).
FORMULA
Numbers k such that A062068(k) = A007947(k).
EXAMPLE
2 is a member, since sigma(2) = 3, tau(3) = 2 and rad(2) = 2.
65856 is a member, since 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
Cf. A000005 (tau), A000203 (sigma) A007947 (rad), A062068.
Sequence in context: A015888 A339793 A343736 * A075122 A018333 A044954
KEYWORD
nonn
AUTHOR
Michel Lagneau, Feb 22 2010
EXTENSIONS
a(31)-a(38) from Donovan Johnson, Jan 14 2012
STATUS
approved