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A061708

Smallest number whose square has (2n - 1)^2 divisors.

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

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OFFSET

1,2

COMMENTS

a(n) <= 6^(n-1); 36^(n-1) has (2n-1)^2 divisors for all n.

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..68

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.