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 A187284 a(n) = round(log(lcm(1,...,n))) - n. 1
 0, -1, -1, -1, -2, -1, -2, -1, -1, -1, -2, -1, -2, 0, -1, -2, -3, -1, -2, 0, -1, -2, -3, -1, -2, -1, -2, -2, -3, -1, -2, 1, 1, 0, -1, -2, -3, -1, -2, -3, -4, -1, -2, 1, 0, -1, -2, 1, 0, 0, -1, -2, -3, 0, -1, -2, -3, -4, -5, -1, -2, 1, 0, -1, -2, -3, -4, 0, -1, -2, -3, 0, -1, 2, 1 (list; graph; refs; listen; history; text; internal format)
 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 Cf. A003418. Sequence in context: A266871 A331290 A060500 * A160198 A207709 A131718 Adjacent sequences:  A187281 A187282 A187283 * A187285 A187286 A187287 KEYWORD sign AUTHOR Ben Branman, Mar 07 2011 STATUS approved

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Last modified June 28 04:00 EDT 2022. Contains 354903 sequences. (Running on oeis4.)