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A135568
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a(n) = floor( Product_{i=1..n} prime(i)/i ).
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3
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1, 2, 3, 5, 8, 19, 41, 101, 240, 614, 1782, 5024, 15492, 48859, 150069, 470216, 1557591, 5405758, 18319515, 64600395, 229331402, 797199637, 2862671427, 10330509932, 38308974332, 148638820408
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OFFSET
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0,2
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COMMENTS
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Does there exist an n such that (the product of the first n primes)/n! is an integer for n>3?
The answer to the question above is obviously no: for n>3 the denominator is a multiple of 4. - Emeric Deutsch, Mar 14 2008
Product_{i=1..n} (p_i/i) is the volume of the n-dimensional simplex with its n+1 vertices at (0, 0, 0, ..., 0), (p_1, 0, 0, ..., 0), (0, p_2, 0, ..., 0), (0, 0, p_3, ..., 0), ..., (0, 0, 0, ..., p_n) in Cartesian coordinates, where p_i is the i-th prime. - Ya-Ping Lu, Sep 21 2020
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LINKS
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FORMULA
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a(n) = floor(product of the first n primes/n!).
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EXAMPLE
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a(5) = floor(2*3*5*7*11/5!) = floor(2310/120) = 19.
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MAPLE
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a:=proc(n) options operator, arrow: floor(mul(ithprime(i)/i, i=1..n)) end proc: seq(a(n), n=1..25); # Emeric Deutsch, Mar 14 2008
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MATHEMATICA
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Table[Floor[Product[Prime[i]/i, {i, n}]], {n, 0, 25}] (* G. C. Greubel, Oct 19 2016 *)
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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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