A061300 Least number whose number of divisors is n!.

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

Offset

0,3

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

Links

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

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.

Example

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

Crossrefs

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

Cf. A140635.

Sequence in context: A012624 A335829 A061307 * A079264 A006939 A152686

Adjacent sequences: A061297 A061298 A061299 * A061301 A061302 A061303

Keyword

nonn,hard

Author

Amarnath Murthy and Labos Elemer, Apr 26 2001

Extensions

More terms from David Wasserman, Jun 13 2002

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

Status

approved