OFFSET
0,5
COMMENTS
A number has equal prime exponents iff it is a power of a squarefree number. We call such numbers uniform, so a(n) is n! divided by the maximum uniform divisor of n!.
After the first three terms, is this sequence strictly increasing?
LINKS
Amiram Eldar, Table of n, a(n) for n = 0..500
EXAMPLE
The sequence of terms together with their prime signatures begins:
1: ()
1: ()
1: ()
1: ()
3: (1)
4: (2)
20: (2,1)
24: (3,1)
192: (6,1)
280: (3,1,1)
2800: (4,2,1)
17280: (7,3,1)
61600: (5,2,1,1)
207360: (9,4,1)
1976832: (9,3,1,1)
28028000: (5,3,2,1,1)
448448000: (9,3,2,1,1)
696729600: (14,5,2,1)
3811808000: (8,3,2,1,1,1)
MATHEMATICA
Table[n!/Max@@Select[Divisors[n!], SameQ@@Last/@FactorInteger[#]&], {n, 0, 15}]
CROSSREFS
A336415 counts these divisors.
A336617 is the version for distinct prime exponents.
A336618 is the quotient n!/a(n).
A047966 counts uniform partitions.
A071625 counts distinct prime exponents.
A130091 lists numbers with distinct prime exponents.
A181796 counts divisors with distinct prime exponents.
A319269 counts uniform factorizations.
A327524 counts factorizations of uniform numbers into uniform numbers.
A327527 counts uniform divisors.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 30 2020
STATUS
approved