A280736 Denominator of Product_{k=1..n-1} k^(2k-n-1).

1, 2, 1, 6, 1, 16, 9, 5, 1, 16, 1, 28, 225, 2048, 1, 729, 1, 125, 49, 11, 1, 55296, 625, 13, 59049, 43904, 1, 8, 1, 67108864, 121, 17, 2401, 1, 1, 19, 169, 1, 1, 16807, 1, 1331, 36905625, 23, 1, 67108864, 117649, 9765625, 23409, 2197, 1, 94143178827, 14641, 262144, 361, 29, 1, 1024

Offset

1,2

Comments

Paul M. Jane observed in an email message to N. J. A. Sloane on Jan 10 2016 that the expression (n-1)!^(n-3) / Product_{k=1..n-2} k!^2 appears to be an integer if and only if n is a prime. That expression can be simplified to give Product_{k=1..n-1} k^(2k-n-1), and the result then follows from Vandendriessche and Lee, Problem A13 (compare A182484, which gives the values at the primes).

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..500

Peter Vandendriessche and Hojoo Lee, Problems in elementary number theory, Problem A13

Example

1, 3/2, 4, 125/6, 225, 84035/16, 2458624/9, 162030456/5, 8930250000, ...

Mathematica

Denominator@Table[Product[k^(2 k - n - 1), {k, 1, n - 1}], {n, 3, 35}] (* Vincenzo Librandi, Jan 12 2017 *)

Crossrefs

Cf. A182484, A280735.

Sequence in context: A322672 A363595 A225769 * A279095 A186283 A307374

Adjacent sequences: A280733 A280734 A280735 * A280737 A280738 A280739

Keyword

nonn,frac

Author

N. J. A. Sloane, Jan 10 2017

Status

approved