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A078560
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Denominator of Product_{i=1..n} (p_i+1)/(p_i-1). Numerators are in A078559.
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2
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1, 1, 1, 1, 5, 5, 10, 1, 11, 11, 11, 11, 55, 5, 115, 1495, 8671, 43355, 476905, 16691675, 16691675, 43398355, 254190365, 559218803, 559218803, 13980470075, 1075420775, 56997301075, 1036314565, 1036314565, 1036314565, 6123676975
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OFFSET
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1,5
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COMMENTS
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According to Koninck (2009), a(8) is the largest value of this sequence known to be 1 (meaning that the product is an integer). [Alonso del Arte, Aug 23 2011]
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REFERENCES
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R. K. Guy, Unsolved Problems in Number Theory, B48.
J.-M. De Koninck, Those Fascinating Numbers, Amer. Math. Soc., 2009, p. 6.
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LINKS
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FORMULA
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MAPLE
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Q:= 1: p:= 1:
for n from 1 to 100 do
p:= nextprime(p);
Q:= Q * (p+1)/(p-1);
A[n]:= denom(Q);
od: seq(A[i], i=1..100); #
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MATHEMATICA
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Denominator[Table[Product[(Prime[i] + 1)/(Prime[i] - 1), {i, n}], {n, 30}]] (* Alonso del Arte, Aug 23 2011 *)
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PROG
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(PARI) a(n) = denominator(prod(i=1, n, (prime(i)+1)/(prime(i)-1))); \\ Michel Marcus, May 11 2018
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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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EXTENSIONS
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STATUS
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approved
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