A061300 Least number whose number of divisors is n!.

1, 1, 2, 12, 360, 55440, 61261200, 293318625600, 6064949221531200, 1315675499575984747200, 1130066578473302698988760000, 8029566026151577210973143393920000, 44532446925432190155112500678140561280000, 89867631285897528426742043782255216503577152000000

Offset: 0

Author

Amarnath Murthy and Labos Elemer, Apr 26 2001

Keywords

• nonn
• hard

Comments

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

Conjecture is confirmed for n <= 30. - Max Alekseyev, Sep 05 2023

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

Examples

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

Links

• Max Alekseyev, Table of n, a(n) for n = 0..30

Crossrefs

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

Cf. A140635.

Formula

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

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

Extensions

More terms from David Wasserman, Jun 13 2002

Terms a(12) onward from Max Alekseyev, Sep 05 2023