A078560 - OEIS

%I #20 May 11 2018 17:51:50

%S 1,1,1,1,5,5,10,1,11,11,11,11,55,5,115,1495,8671,43355,476905,

%T 16691675,16691675,43398355,254190365,559218803,559218803,13980470075,

%U 1075420775,56997301075,1036314565,1036314565,1036314565,6123676975

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

%C 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 R. K. Guy, Unsolved Problems in Number Theory, B48.

%D J.-M. De Koninck, Those Fascinating Numbers, Amer. Math. Soc., 2009, p. 6.

%H Robert Israel, <a href="/A078560/b078560.txt">Table of n, a(n) for n = 1..1703</a>

%H F. Smarandache, <a href="http://www.gallup.unm.edu/~smarandache/OPNS.pdf">Only Problems, Not Solutions!</a>.

%F a(n) = A005867(n)/A078558(n).

%p Q:= 1: p:= 1:

%p for n from 1 to 100 do

%p   p:= nextprime(p);

%p   Q:= Q * (p+1)/(p-1);

%p   A[n]:= denom(Q);

%p od: seq(A[i], i=1..100); #

%t Denominator[Table[Product[(Prime[i] + 1)/(Prime[i] - 1), {i, n}], {n, 30}]] (* _Alonso del Arte_, Aug 23 2011 *)

%o (PARI) a(n) = denominator(prod(i=1, n, (prime(i)+1)/(prime(i)-1))); \\ _Michel Marcus_, May 11 2018

%Y Cf. A000203, A002110, A000005, A005867, A054640, A020492, A078558, A078559.

%K nonn,frac

%O 1,5

%A _Labos Elemer_, Dec 06 2002

%E Improved definition from _Franklin T. Adams-Watters_, Dec 02 2005