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

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

Offset

1,5

Comments

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]

References

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

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

Links

Robert Israel, Table of n, a(n) for n = 1..1703

F. Smarandache, Only Problems, Not Solutions!.

Formula

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

Maple

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); #

Mathematica

Denominator[Table[Product[(Prime[i] + 1)/(Prime[i] - 1), {i, n}], {n, 30}]] (* Alonso del Arte, Aug 23 2011 *)

Prog

(PARI) a(n) = denominator(prod(i=1, n, (prime(i)+1)/(prime(i)-1))); \\ Michel Marcus, May 11 2018

Crossrefs

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

Sequence in context: A351292 A290240 A245088 * A331064 A040021 A339720

Adjacent sequences: A078557 A078558 A078559 * A078561 A078562 A078563

Keyword

nonn,frac

Author

Labos Elemer, Dec 06 2002

Extensions

Improved definition from Franklin T. Adams-Watters, Dec 02 2005

Status

approved