|
| |
|
|
A055773
|
|
Product of primes p for which p divides n! but p^2 does not (i.e. ord_p(n!)=1).
|
|
13
| |
|
|
1, 2, 6, 3, 15, 5, 35, 35, 35, 7, 77, 77, 1001, 143, 143, 143, 2431, 2431, 46189, 46189, 46189, 4199, 96577, 96577, 96577, 7429, 7429, 7429, 215441, 215441, 6678671, 6678671, 6678671, 392863, 392863, 392863, 14535931, 765049, 765049, 765049
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,2
|
|
|
COMMENTS
| Squarefree part of n! divided by GCD[Q,F], where Q is the largest square divisor and F is the squarefree part of n!. - Labos E. (labos(AT)ana.sote.hu), Jul 12 2000
a(1) = 1, a(n) = n*a(n-1) if n is a prime else a(n) = least integer multiple of a(n-1)/n. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Apr 29 2004
Let P(i) denote the primorial number A034386(i). Then a(n) = P(n)/P(floor(n/2)). - Peter Luschny, Mar 5 2011.
|
|
|
LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..200
F. J. van de Bult, D. C. Gijswijt, J. P. Linderman, N. J. A. Sloane and A. R. Wilks, A Slow-Growing Sequence Defined by an Unusual Recurrence, J. Integer Sequences, Vol. 10 (2007), #07.1.2.
|
|
|
FORMULA
| a(n) = Numerator(A056040(n)^2/n!).
a(n) = Numerator(A056040(n)/floor(n/2)!^2).
a(n) = Numerator(n!/floor(n/2)!^4). [Peter Luschny, Jul 30 2011]
a(n) = product of primes p such that n/2 < p <= n. - Klaus Brockhaus, May 02 2004
a(n)=A055204(n)/A055230(n)=A055231(n!)=n!/([A007913(n!)*A055229[n])
|
|
|
EXAMPLE
| n=13, 13!=6227020800, A007913(13!)=4608*4608, A008833(13!)=3003, g(13!)=GCD(4608,3003)=3, so a(13)=13!/(4608*4608*3)=1001.
|
|
|
MAPLE
| a := n -> mul(k, k=select(isprime, [$iquo(n, 2)+1..n])); [Peter Luschny, Jun 20 2009]
A055773 := n -> numer(n!/iquo(n, 2)!^4); [Peter Luschny, Jul 30 2011]
|
|
|
PROG
| (PARI) q=1; for(n=2, 41, print1(q, ", "); q=if(isprime(n), q*n, q/gcd(q, n))) - Klaus Brockhaus, May 02 2004
(PARI) a(n) = k=1; forprime(p=nextprime(n\2+1), precprime(n), k=k*p); k - Klaus Brockhaus, May 02 2004
|
|
|
CROSSREFS
| Cf. A000188, A008833, A007913, A055229, A055231 (for n), A055071, A055204, A055230, A055773 (for n!).
Cf. A094299, A094302. Cf. A193477.
Sequence in context: A094426 A094302 A094300 * A111866 A072155 A094299
Adjacent sequences: A055770 A055771 A055772 * A055774 A055775 A055776
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Labos E. (labos(AT)ana.sote.hu), Jul 12 2000
|
|
|
EXTENSIONS
| Simpler definition from Dion Gijswijt (gijswijt(AT)science.uva.nl), Jan 07 2007
Entry revised by N. J. A. Sloane (njas(AT)research.att.com), Jan 07 2007
|
| |
|
|
