OFFSET
1,2
COMMENTS
a(11), if it exists, is greater than 10^12. - Ryan Propper, Oct 10 2005
Comments from Lambert Klasen (lambert.klasen(AT)gmx.net), Oct 25 2005: "Sequence is infinite. For a prime p, a(p) has p^p as a factor. Factoring the a(n) gives the pattern for the exponents:
[2, 1]
[2, 2]
[2, 1; 3, 3]
[2, 5; 3, 1]
[2, 2; 3, 1; 5, 5]
[2, 2; 3, 1; 5, 1]
[2, 2; 3, 1; 5, 1; 7, 7]
[2, 10; 3, 1; 5, 1; 7, 1]
[2, 3; 3, 10; 5, 1; 7, 1]
[2, 3; 3, 2; 5, 1; 7, 1]
[2, 3; 3, 2; 5, 1; 7, 1; 11, 11]
[2, 3; 3, 2; 5, 1; 7, 1; 11, 1]
[2, 3; 3, 2; 5, 1; 7, 1; 11, 1; 13, 13]
[2, 3; 3, 2; 5, 1; 7, 1; 11, 1; 13, 1]
[2, 3; 3, 2; 5, 1; 7, 1; 11, 1; 13, 1]
[2, 19; 3, 2; 5, 1; 7, 1; 11, 1; 13, 1]
[2, 4; 3, 2; 5, 1; 7, 1; 11, 1; 13, 1; 17, 17]
[2, 4; 3, 2; 5, 1; 7, 1; 11, 1; 13, 1; 17, 1]
[2, 4; 3, 2; 5, 1; 7, 1; 11, 1; 13, 1; 17, 1; 19, 19]
[2, 4; 3, 2; 5, 1; 7, 1; 11, 1; 13, 1; 17, 1; 19, 1]
[2, 4; 3, 2; 5, 1; 7, 1; 11, 1; 13, 1; 17, 1; 19, 1]
[2, 4; 3, 2; 5, 1; 7, 1; 11, 1; 13, 1; 17, 1; 19, 1]
[2, 4; 3, 2; 5, 1; 7, 1; 11, 1; 13, 1; 17, 1; 19, 1; 23, 23]."
EXAMPLE
(1*4*54*96)^(1/4) = (20736)^(1/4) = 12.
a(5) = 37500 = 2^2 * 3 * 5^5.
a(11) = 718985409939720 = 2^3 * 3^2 * 5 * 7 * 11^11.
MATHEMATICA
p = 1; Do[k = 1; While[ !IntegerQ[(p*k*n)^(1/n)], k++ ]; Print[k*n]; p *= (k*n), {n, 1, 10}] (* Ryan Propper, Oct 10 2005 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Jun 08 2004
EXTENSIONS
More terms from Ryan Propper, Oct 10 2005
a(11) onwards from Lambert Klasen (lambert.klasen(AT)gmx.net), Oct 25 2005
STATUS
approved