

A182484


a(n) = Product_{k=1..p1} k^(2kp1), where p = prime(n).


2




OFFSET

1,3


COMMENTS

a(n) is always an integer [Vandendriessche and Lee, Problem A13].  N. J. A. Sloane, Jan 10 2017
a(9) contains 70 digits; a(10) contains 121 digits; a(11) contains 142 digits; a(12) contains 213 digits; a(13) contains 269 digits.
Conjecture (false!): a(n) = Product_{k=1..p1} k^(2kp1) is a perfect square if, and only if p = prime(n).
The conjecture above is disproved by the counterexample p=63 for which the indicated product is a square, yet 63 is not a prime. [John W. Layman, May 01 2012]


LINKS



EXAMPLE

a(3) = 4 because, for prime(3) = 5,
Product_{k=1..4} k^(2k6) = 1^(4)*2^(2)*3^0*4^2 = 4.


MAPLE

with(numtheory):seq(product(k^(2*kithprime(n)1), k=1.. ithprime(n)1), n=1..9);


MATHEMATICA

Table[Product[k^(2*k  n  1), {k, n1}], {n, Prime[Range[8]]}] (* T. D. Noe, May 01 2012 *)


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



