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A061708
Smallest number whose square has (2n - 1)^2 divisors.
1
1, 6, 36, 216, 210, 7776, 46656, 1260, 1679616, 10077696, 7560, 362797056, 44100, 18480, 78364164096, 470184984576, 272160, 264600, 101559956668416, 1632960, 3656158440062976, 21936950640377856, 180180, 789730223053602816, 9261000, 58786560, 170581728179578208256
OFFSET
1,2
COMMENTS
a(n) <= 6^(n-1); 36^(n-1) has (2n-1)^2 divisors for all n.
LINKS
FORMULA
a(n) = Min_{x : d(x^2) = (2n-1)^2};
a(n) = Min_{x : A000005(A000290(x)) = A000290(A005408(n))}.
EXAMPLE
For n = 8, a(8) = 1260 = 2*2*3*3*5*7 and d(1260^2) = d(2*2*2*2*3*3*3*3*5*5*7*7) = 225 = (2*8-1)^2.
For n = 14, a(14) = 18480 and d((2*2*2*2*2*2*2*2*3*5*7*11)^2) = 729 = (2*14-1)^2.
KEYWORD
nonn
AUTHOR
Labos Elemer, Jun 19 2001
EXTENSIONS
More terms from David Wasserman, Jun 24 2002
Edited by Charlie Neder, Jun 03 2019
a(26)-a(27) from Amiram Eldar, Dec 03 2023
STATUS
approved