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A048855
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Number of integers up to n! relatively prime to n!.
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21
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1, 1, 1, 2, 8, 32, 192, 1152, 9216, 82944, 829440, 8294400, 99532800, 1194393600, 16721510400, 250822656000, 4013162496000, 64210599936000, 1155790798848000, 20804234379264000, 416084687585280000, 8737778439290880000, 192231125664399360000
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OFFSET
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0,4
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COMMENTS
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Rephrasing the Quet formula: Begin with 1. Then, if n + 1 is prime subtract 1 and multiply. If n+1 is not prime, multiply. Continue writing each product. Thus the sequence would begin 1, 2, 8, . . . . The first product is 1*(2 - 1), second is 1*(3 - 1), and third is 2*4. - Enoch Haga, May 06 2009
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REFERENCES
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Ronald L. Graham, D. E. Knuth and Oren Patashnik, "Concrete Mathematics, A Foundation for Computer Science," Addison-Wesley Publ. Co., Reading, MA, 1989, page 134.
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LINKS
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FORMULA
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If n is composite, then a(n) = a(n-1)*n. If n is prime, then a(n) = a(n-1)*(n-1). - Leroy Quet, May 24 2007
Under the Riemann Hypothesis, a(n) = n! / (e^gamma * log n) * (1 + O(log n/sqrt(n))). - Charles R Greathouse IV, May 12 2011
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MAPLE
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with(numtheory):a:=n->phi(n!): seq(a(n), n=0..20); # Zerinvary Lajos, Oct 07 2007
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MATHEMATICA
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PROG
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(Sage) [euler_phi(factorial(n)) for n in range(0, 21)] # Zerinvary Lajos, Jun 06 2009
(Python)
from math import factorial, prod
from sympy import primerange
from fractions import Fraction
def A048855(n): return (factorial(n)*prod(Fraction(p-1, p) for p in primerange(n+1))).numerator # Chai Wah Wu, Jul 06 2022
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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