OFFSET
0,5
COMMENTS
The prime number theorem implies that lcm(1,2,...,n) = exp(n(1+o(1))) as n -> infinity.
The sequence seems to exhibit significant unpredictability.
LINKS
T. D. Noe, Table of n, a(n) for n = 0..10000
FORMULA
a(n) = round(log(A003418(n))) - n.
EXAMPLE
lcm(1,2,...20)=232792560, log(232792560)=19.2657, round(19.2657-20)=-1, so a(20)=-1.
MATHEMATICA
nn=1000; Round[Flatten[{Log /@ FoldList[LCM, 1, Range@nn] - Range[0, nn}]]
Join[{0}, Table[Round[Log[LCM@@Range[n]]]-n, {n, 80}]] (* Harvey P. Dale, Jan 08 2020 *)
CROSSREFS
KEYWORD
sign
AUTHOR
Ben Branman, Mar 07 2011
STATUS
approved