A187284 a(n) = round(log(lcm(1,...,n))) - n.

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

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