The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A182484 a(n) = Product_{k=1..p-1} k^(2k-p-1), where p = prime(n). 2
 1, 1, 4, 225, 8930250000, 9001015156742400, 377177413291384771899817984000000, 17617791710438789613561393948051882397138944 (list; graph; refs; listen; history; text; internal format)
 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..p-1} k^(2k-p-1) 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 Table of n, a(n) for n=1..8. Peter Vandendriessche and Hojoo Lee, Problems in elementary number theory, Problem A13 EXAMPLE a(3) = 4 because, for prime(3) = 5, Product_{k=1..4} k^(2k-6) = 1^(-4)*2^(-2)*3^0*4^2 = 4. MAPLE with(numtheory):seq(product(k^(2*k-ithprime(n)-1), k=1.. ithprime(n)-1), n=1..9); MATHEMATICA Table[Product[k^(2*k - n - 1), {k, n-1}], {n, Prime[Range[8]]}] (* T. D. Noe, May 01 2012 *) CROSSREFS Sequence in context: A211610 A364481 A042539 * A159281 A290346 A113255 Adjacent sequences: A182481 A182482 A182483 * A182485 A182486 A182487 KEYWORD nonn AUTHOR Michel Lagneau, May 01 2012 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 15 22:50 EDT 2024. Contains 373412 sequences. (Running on oeis4.)