A121161 a(n) is the nearest integer to log(lcm(1,2,3,...,10^n)).

0, 8, 94, 997, 10013, 100052, 999587, 9998539, 99998243, 1000001596, 10000042120

Offset

0,2

Links

Table of n, a(n) for n=0..10.

Andrew Granville and Greg Martin, Prime Number Races, arXiv:math/0408319 [math.NT], 2004 (see page 11).

Formula

For asymptotics see A003418.

a(n) = Sum_{i=1..PrimePi(10^n)} log(p_i^e_i), where e is the maximum exponent such that p^e < 10^n. - Robert G. Wilson v, Aug 16 2006

Mathematica

f[n_] := Block[{s = 0, i = 1, j = PrimePi[10^n], m = 10^n}, While[i <= j, p = Prime@i; s = s + N[Floor[ Log[p, m]]Log[p], 12]; i++ ]; Round@s]; Do[ Print[f@n], {n, 0, 8}] (* Robert G. Wilson v, Aug 16 2006 *)

Crossrefs

Cf. A003418.

Sequence in context: A299339 A299846 A214385 * A360200 A098269 A010565

Adjacent sequences: A121158 A121159 A121160 * A121162 A121163 A121164

Keyword

nonn,more

Author

Lekraj Beedassy, Aug 13 2006

Extensions

More terms from Robert G. Wilson v, Aug 16 2006

a(9)-a(10) from Robert G. Wilson v, Sep 03 2012

Status

approved