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

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.
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.

Crossrefs

Cf. A000005, A000290, A005179, A005408, A016017, A025281, A048691.

Sequence in context: A199525 A074436 A036162 * A216127 A337970 A124535

Adjacent sequences: A061705 A061706 A061707 * A061709 A061710 A061711

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