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A078560 Denominator of Product_{i=1..n} (p_i+1)/(p_i-1). Numerators are in A078559.

%I A078560 #20 May 11 2018 17:51:50
%S A078560 1,1,1,1,5,5,10,1,11,11,11,11,55,5,115,1495,8671,43355,476905,
%T A078560 16691675,16691675,43398355,254190365,559218803,559218803,13980470075,
%U A078560 1075420775,56997301075,1036314565,1036314565,1036314565,6123676975
%N A078560 Denominator of Product_{i=1..n} (p_i+1)/(p_i-1). Numerators are in A078559.
%C A078560 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]
%D A078560 R. K. Guy, Unsolved Problems in Number Theory, B48.
%D A078560 J.-M. De Koninck, Those Fascinating Numbers, Amer. Math. Soc., 2009, p. 6.
%H A078560 Robert Israel, <a href="/A078560/b078560.txt">Table of n, a(n) for n = 1..1703</a>
%H A078560 F. Smarandache, <a href="http://www.gallup.unm.edu/~smarandache/OPNS.pdf">Only Problems, Not Solutions!</a>.
%F A078560 a(n) = A005867(n)/A078558(n).
%p A078560 Q:= 1: p:= 1:
%p A078560 for n from 1 to 100 do
%p A078560   p:= nextprime(p);
%p A078560   Q:= Q * (p+1)/(p-1);
%p A078560   A[n]:= denom(Q);
%p A078560 od: seq(A[i], i=1..100); #
%t A078560 Denominator[Table[Product[(Prime[i] + 1)/(Prime[i] - 1), {i, n}], {n, 30}]] (* _Alonso del Arte_, Aug 23 2011 *)
%o A078560 (PARI) a(n) = denominator(prod(i=1, n, (prime(i)+1)/(prime(i)-1))); \\ _Michel Marcus_, May 11 2018
%Y A078560 Cf. A000203, A002110, A000005, A005867, A054640, A020492, A078558, A078559.
%K A078560 nonn,frac
%O A078560 1,5
%A A078560 _Labos Elemer_, Dec 06 2002
%E A078560 Improved definition from _Franklin T. Adams-Watters_, Dec 02 2005