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A163644
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Product of primes which do not exceed n and do not divide the swinging factorial n$ (A056040).
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0
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1, 1, 1, 1, 1, 1, 3, 3, 3, 1, 5, 5, 5, 5, 35, 7, 7, 7, 21, 21, 105, 5, 55, 55, 165, 33, 429, 143, 1001, 1001, 1001, 1001, 1001, 91, 1547, 221, 221, 221, 4199, 323, 323, 323, 2261, 2261, 24871, 24871, 572033, 572033, 572033, 81719, 408595, 24035, 312455
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,7
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COMMENTS
| a(n) = primorial(n) / rad(n$) = A034386(n) / A163641(n).
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REFERENCES
| Peter Luschny, "Divide, swing and conquer the factorial and the lcm{1,2,...,n}", preprint, April 2008.
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LINKS
| Peter Luschny, Swinging Factorial.
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EXAMPLE
| a(20) = 105 because in the prime-factorisation of 20$ the primes 3, 5 and 7 are missing and 3*5*7 = 105.
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MAPLE
| a := proc(n) local p; mul(p, p=select(isprime, {$1..n})
minus numtheory[factorset](n!/iquo(n, 2)!^2)) end:
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CROSSREFS
| Cf. A056040, A034386, A163641, A056610.
Sequence in context: A123073 A059289 A201277 * A014465 A155969 A076237
Adjacent sequences: A163641 A163642 A163643 * A163645 A163646 A163647
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KEYWORD
| nonn
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AUTHOR
| Peter Luschny (peter(AT)luschny.de), Aug 02 2009
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