OFFSET
0,5
COMMENTS
The author proposes to denote this sequence lcm_{p}(n) as lcm(n) = lcm({1,2,..n}) = exp(Sum_{k=1..n} Sum_{d|k} moebius(d)*log(k/d)).
For n > 0 the a(n) are the partial products of A205959(n), which is the exponential of a modified von Mangoldt function where the divisors are restricted to prime divisors.
LINKS
Michel Marcus, Table of n, a(n) for n = 0..400
Peter Luschny, The von Mangoldt Transformation.
FORMULA
a(n) = Product_{p prime, p<=n} (floor(n/p)!). - Ridouane Oudra, Nov 22 2021
MAPLE
MATHEMATICA
a[n_] := Exp[-Sum[ MoebiusMu[p] Log[k/p], {k, 1, n}, {p, FactorInteger[k][[All, 1]]}]]; Table[a[n], {n, 0, 27}] (* Jean-François Alcover, Jun 27 2013 *)
PROG
(Sage)
def A205957(n) : return simplify(exp(-add(add(moebius(p)*log(k/p) for p in prime_divisors(k)) for k in (1..n))))
(PARI) a(n)=prod(k=4, n, my(f=factor(k)[, 1]); prod(i=1, #f, k/f[i])) \\ Charles R Greathouse IV, Jun 27 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
Peter Luschny, Sep 01 2012
STATUS
approved