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A085078
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The largest number with the prime signature of n! using primes <= n.
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0
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1, 2, 6, 54, 750, 11250, 360150, 123531450, 3088286250, 64854011250, 77201350992150, 65389544290351050, 32637304517036749530, 2121424793607388719450, 163349709107768931397650
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OFFSET
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1,2
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COMMENTS
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n! is the smallest number with that prime signature. E.g. 720 = 2^4*3^2*5. (Can we name a(n) as the eldest brother of n!?) Subsidiary sequence: Total number of distinct numbers with prime signature that of n! having prime divisors less than or equal to n.
Contribution from Reikku Kulon, Sep 18 2008: (Start)
This is n! with prime exponents reversed. Perhaps it should be denoted with an inverted exclamation mark: (inverted-!)n
7! = 5040 = 2^4 * 3^2 * 5^1 * 7^1
(inverted-!)7 = 360150 = 2^1 * 3^1 * 5^2 * 7^4 (End)
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LINKS
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Table of n, a(n) for n=1..15.
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EXAMPLE
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6!= 720 = 2^4*3^2*5, hence a(6) = 5^4*3^2*2 = 11250.
for a(8), 40320= 2^7*3^2*5*7 -> 7^7*5^2*3*2 =123531450.
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PROG
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(PARI) for (n = 1, 20, f = factor(n!); c = matsize(f)[1]; a = prod(i = 1, c, f[i, 1]^f[c + 1 - i, 2]); print(a)); (Wasserman)
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CROSSREFS
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Cf. A000142.
Cf. A000040 [From Reikku Kulon, Sep 18 2008]
Sequence in context: A027258 A156340 A219692 * A152543 A122593 A153450
Adjacent sequences: A085075 A085076 A085077 * A085079 A085080 A085081
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jul 01 2003
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EXTENSIONS
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More terms from David Wasserman, Jan 14 2005
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STATUS
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approved
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