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A336619
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a(n) = n!/d where d is the maximum divisor of n! with equal prime exponents.
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4
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1, 1, 1, 1, 3, 4, 20, 24, 192, 280, 2800, 17280, 61600, 207360, 1976832, 28028000, 448448000, 696729600, 3811808000, 12541132800, 250822656000, 5069704640000, 111533502080000, 115880067072000, 2781121609728000, 21277380032004096, 447206762741760000
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OFFSET
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0,5
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COMMENTS
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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?
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LINKS
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FORMULA
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EXAMPLE
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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)
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MATHEMATICA
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Table[n!/Max@@Select[Divisors[n!], SameQ@@Last/@FactorInteger[#]&], {n, 0, 15}]
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CROSSREFS
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A336617 is the version for distinct prime exponents.
A071625 counts distinct prime exponents.
A072774 gives Heinz numbers of uniform partitions, with nonprime terms A182853.
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.
Factorial numbers: A000142, A007489, A022559, A027423, A048656, A071626, A108731, A325272, A325273, A325617, A336414, A336416.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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