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A117481
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a(n) = n*(n-1)*(n-2)*(n-3)*...*(n-k) such that (n-k) is the largest prime smaller than n.
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1
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1, 2, 6, 12, 60, 30, 210, 56, 504, 5040, 55440, 132, 1716, 182, 2730, 43680, 742560, 306, 5814, 380, 7980, 175560, 4037880, 552, 13800, 358800, 9687600, 271252800, 7866331200, 870, 26970, 992, 32736, 1113024, 38955840, 1402410240, 51889178880
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = Product_{k = prevprime(n)..n} k, for n>=3 with a(1)=1, a(2)=2 and where prevprime = A151799. - Wesley Ivan Hurt, Dec 12 2021
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EXAMPLE
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a(10) = 10*9*8*7 = 5040 because 7 is the largest prime smaller than 10.
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MATHEMATICA
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a[1] = 1; a[2] = 2; a[n_] := n!/(NextPrime[n, -1] - 1)!; Array[a, 30] (* Amiram Eldar, Feb 08 2021 *)
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PROG
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(PARI) a(n) = if (n<=2, n, prod(k=0, n-precprime(n-1), n-k)); \\ Michel Marcus, Feb 09 2021
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CROSSREFS
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Cf. A151799 (prevprime v.2), A286900 (sum of the numbers from n to nextprime(n)).
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KEYWORD
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AUTHOR
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Luc Stevens (lms022(AT)yahoo.com), Apr 25 2006
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EXTENSIONS
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STATUS
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approved
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