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A090585
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Numerator of (Sum_{k=1..n} k) / (Product_{k=1..n} k).
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13
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1, 3, 1, 5, 1, 7, 1, 1, 1, 11, 1, 13, 1, 1, 1, 17, 1, 19, 1, 1, 1, 23, 1, 1, 1, 1, 1, 29, 1, 31, 1, 1, 1, 1, 1, 37, 1, 1, 1, 41, 1, 43, 1, 1, 1, 47, 1, 1, 1, 1, 1, 53, 1, 1, 1, 1, 1, 59, 1, 61, 1, 1, 1, 1, 1, 67, 1, 1, 1, 71, 1, 73, 1, 1, 1, 1, 1, 79, 1, 1, 1, 83, 1
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OFFSET
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1,2
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COMMENTS
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If the offset is set to 2 then [a(n) <> 1] is the indicator function of the odd primes ([] Iverson bracket). [Peter Luschny, Jul 05 2009]
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LINKS
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FORMULA
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Also for n>1, a(n) is a numerator of determinant of (n-1) X (n-1) matrix with M(i,j) = (i+2)/(i+1) if i=j, otherwise 1. E.g., a(2) = Numerator[Det[{{3/2}}]] = Numerator[3/2] = 3. a(3) = Numerator[Det[{{3/2,1},{1,4/3}}]] = Numerator[1/1] = 1. a(4) = Numerator[Det[{{3/2,1,1},{1,4/3,1},{1,1,5/4}}]] = Numerator[5/12] = 5. - Alexander Adamchuk, May 26 2006
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EXAMPLE
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For n=5, (1+2+3+4+5)/(1*2*3*4*5) = 15/120 = 1/8, so a(5) = 1. For n=6, (1+2+3+4+5+6)/(1*2*3*4*5*6) = 21/720 = 7/240, so a(6) = 7. - Michael B. Porter, Jul 02 2016
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MAPLE
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MATHEMATICA
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With[{nn=100}, Numerator[Accumulate[Range[nn]]/Rest[FoldList[Times, 1, Range[nn]]]]] (* Harvey P. Dale, Sep 09 2014 *)
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PROG
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(PARI) for(n=1, 100, print1(gcd(n*(n+1)/2, round(factorial(n))+1), ", ")); \\ Jaume Oliver Lafont, Jan 23 2009
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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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