login
A078560
Denominator of Product_{i=1..n} (p_i+1)/(p_i-1). Numerators are in A078559.
2
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
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
KEYWORD
nonn,frac
AUTHOR
Labos Elemer, Dec 06 2002
EXTENSIONS
Improved definition from Franklin T. Adams-Watters, Dec 02 2005
STATUS
approved