%I #25 Sep 06 2023 01:11:35

%S 1,1,2,12,360,55440,61261200,293318625600,6064949221531200,

%T 1315675499575984747200,1130066578473302698988760000,

%U 8029566026151577210973143393920000,44532446925432190155112500678140561280000,89867631285897528426742043782255216503577152000000

%N Least number whose number of divisors is n!.

%C a(n) = A037019(n!) for all n <= 12 except for 4. I conjecture that this remains true for all larger n, i.e., 4! is the only "exceptional" factorial (see A037019). - _David Wasserman_, Jun 13 2002

%C Conjecture is confirmed for n <= 30. - _Max Alekseyev_, Sep 05 2023

%C Alternate definition: a(0)=1; for n >= 1, smallest number with same number of divisors as A006939(n-1). - _J. Lowell_, May 20 2008

%H Max Alekseyev, <a href="/A061300/b061300.txt">Table of n, a(n) for n = 0..30</a>

%F a(n) = A005179(n!); for example, A005179(120)=55440.

%F a(n) = Min{x| A000005(x)=n!}; for example, A000005(55440)=120 and 55440 is minimal.

%e a(3) = 12 and tau(12) = 6 = 3!.

%Y Cf. A000005, A005179, A007304, A006939, A037019, A000142, A072066, A009287.

%Y Cf. A140635.

%K nonn,hard

%O 0,3

%A _Amarnath Murthy_ and _Labos Elemer_, Apr 26 2001

%E More terms from _David Wasserman_, Jun 13 2002

%E Terms a(12) onward from _Max Alekseyev_, Sep 05 2023