|
| |
|
|
A163640
|
|
The radical of the swinging factorial A056040 for odd indices.
|
|
1
| |
|
|
1, 6, 30, 70, 210, 462, 6006, 4290, 72930, 461890, 1939938, 4056234, 6760390, 1560090, 6463230, 200360130, 2203961430, 907513530, 33578000610, 22974421470, 941951280270
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
COMMENTS
| Let $ denote the swinging factorial. a(n) is the radical of (2*n+1)$ which is the product of the prime numbers dividing (2*n+1)$. It is the largest squarefree divisor of (2*n+1)$, and so also described as the squarefree kernel of (2*n+1)$.
|
|
|
REFERENCES
| Peter Luschny, "Divide, swing and conquer the factorial and the lcm{1,2,...,n}", preprint, April 2008.
|
|
|
LINKS
| Peter Luschny, Swinging Factorial.
|
|
|
EXAMPLE
| (2*5+1)$ = 2772 = 2^2*3^2*7*11. Therefore a(5) = 2*3*7*11 = 462.
|
|
|
MAPLE
| a := proc(n) local p; mul(p, p=numtheory[factorset]((2*n+1)!/iquo(2*n+1, 2)!^2)) end:
|
|
|
CROSSREFS
| A056040(n) = n$, A163641(n) = rad(n$), A080397(n) = rad((2n)$).
Sequence in context: A145010 A056835 A056836 * A199130 A152743 A038039
Adjacent sequences: A163637 A163638 A163639 * A163641 A163642 A163643
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Peter Luschny (peter(AT)luschny.de), Aug 02 2009
|
| |
|
|
