A061708 - OEIS

%I #20 Dec 03 2023 05:03:00

%S 1,6,36,216,210,7776,46656,1260,1679616,10077696,7560,362797056,44100,

%T 18480,78364164096,470184984576,272160,264600,101559956668416,1632960,

%U 3656158440062976,21936950640377856,180180,789730223053602816,9261000,58786560,170581728179578208256

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

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

%H Amiram Eldar, <a href="/A061708/b061708.txt">Table of n, a(n) for n = 1..68</a>

%F a(n) = Min_{x : d(x^2) = (2n-1)^2};

%F a(n) = Min_{x : A000005(A000290(x)) = A000290(A005408(n))}.

%e 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.

%e 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.

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

%K nonn

%O 1,2

%A _Labos Elemer_, Jun 19 2001

%E More terms from _David Wasserman_, Jun 24 2002

%E Edited by _Charlie Neder_, Jun 03 2019

%E a(26)-a(27) from _Amiram Eldar_, Dec 03 2023