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A271387
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Numerator of prime(n)#/n!, where prime(n)# is the prime factorial function.
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1
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1, 2, 3, 5, 35, 77, 1001, 2431, 46189, 1062347, 30808063, 86822723, 3212440751, 10131543907, 435656388001, 20475850236047, 1085220062510491, 3766351981654057, 229747470880897477, 810162134158954261, 57521511525285752531, 4199070341345859934763, 331726556966322934846277
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OFFSET
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0,2
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LINKS
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Eric Weisstein's World of Mathematics, Primorial
Eric Weisstein's World of Mathematics, Factorial
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FORMULA
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a(n) = prime(n)#/GCD(prime(n)#, n!), where GCD(a, b) is the greatest common divisor.
a(n) = prime(n)#/prime(pi(n))#, where pi(n) is the number of primes <= n.
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EXAMPLE
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1, 2, 3, 5, 35/4, 77/4, 1001/24, 2431/24, 46189/192, 1062347/1728, 30808063/17280, 86822723/17280, 3212440751/207360, 10131543907/207360, 435656388001/2903040, ...
a(8) = 46189, because prime(8)#/8! = (2*3*5*7*11*13*17*19)/(1*2*3*4*5*6*7*8) = 46189/192.
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MATHEMATICA
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Table[Numerator[Product[Prime@ k, {k, n}]/n!], {n, 0, 22}] (* Michael De Vlieger, Apr 08 2016 *)
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PROG
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(PARI) a(n) = numerator(prod(k=1, n, prime(k))/n!); \\ Michel Marcus, Apr 09 2016
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CROSSREFS
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KEYWORD
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nonn,frac
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AUTHOR
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STATUS
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approved
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