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A061300
Least number whose number of divisors is n!.
4
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
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!.
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