A068625 / A048803

Maximilian Hasler maximilian.hasler at gmail.com
Sun Feb 17 21:12:49 CET 2008

```The definition of the following sequence is not completely clear IMHO
: "smallest integer root" = square free kernel ? then it is an
erroneous (a(12)=12a(11) instead of 6 a(11)) duplicate of A048803
(included below), afaics.
The latter, A048803, has a slightly obscure %N which should maybe
better be a %C and be replaced by the %F (if everybody agrees that it
is indeed equivalent to the %N - at least all given terms indeed
correspond to "reduced root / square-free kernel factorial").
Maximilian

%S A068625 1,2,6,12,60,360,2520,5040,15120,151200,1663200,19958400,259459200,
%T A068625 3632428800,54486432000,108972864000,1852538688000,33345696384000,
%U A068625 633568231296000,12671364625920000,266098657144320000
%N A068625 Reduced root factorial of n: product of the smallest
integer root of numbers from
1 to n.
%e A068625 a(8) = 1*2*3*2*5*6*7*2= 5040.
%O A068625 1,2
%A A068625 Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Feb 26 2002

%S A048803 1,1,2,6,12,60,360,2520,5040,15120,151200,1663200,9979200,129729600,
%T A048803 1816214400,27243216000,54486432000,926269344000,5557616064000,
%U A048803 105594705216000,1055947052160000,22174888095360000,487847538097920000
%N A048803 a(0) = 1, a(1) = 1; for n > 1, a(n) = l.c.m { 1, 2, ..., n,
a(1)*a(n-1), a(2)*a(n-2),
..., a(n-1)*a(1) }.
%C A048803 Squarefree factorials: a(1) = 1, a(n+1) = a(n)* largest
squarefree divisor of (n+1).
- Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Nov 28 2004
%D A048803 Paul-Jean Cahen and Jean-Luc Chabert, Integer-valued
Polynomials, AMS, Providence,
RI, 1997. Math. Rev. 98a:13002. See p. 246.
%H A048803 <a href="http://www.research.att.com/~njas/sequences/Sindx_Lc.html#lcm">Index
entries
for sequences related to lcm's</a>
%F A048803 Partial products of A007947.
%o A048803 (PARI) a(n)=local(f); f=n>=0; if(n>1, forprime(p=2,n,f*=p^(n\p))); f
%O A048803 0,3
%A A048803 Christian G. Bower (bowerc(AT)usa.net), Apr 15 1999.
%E A048803 Entry improved by comments from Michael Somos, Nov 24, 2001

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