A078559 -id:A078559 - cp's OEIS frontend

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

Labos Elemer, Dec 06 2002

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]

R. K. Guy, Unsolved Problems in Number Theory, B48.
J.-M. De Koninck, Those Fascinating Numbers, Amer. Math. Soc., 2009, p. 6.

Robert Israel, Table of n, a(n) for n = 1..1703
F. Smarandache, Only Problems, Not Solutions!.

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

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); #

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

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

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

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

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

References

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Formula

Extensions