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a(n) is the nearest integer to log(lcm(1,2,3,...,10^n)).
0

%I #26 Nov 13 2023 12:39:13

%S 0,8,94,997,10013,100052,999587,9998539,99998243,1000001596,

%T 10000042120

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

%H Andrew Granville and Greg Martin, <a href="http://arxiv.org/abs/math/0408319">Prime Number Races</a>, arXiv:math/0408319 [math.NT], 2004 (see page 11).

%F For asymptotics see A003418.

%F 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

%t 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 *)

%Y Cf. A003418.

%K nonn,more

%O 0,2

%A _Lekraj Beedassy_, Aug 13 2006

%E More terms from _Robert G. Wilson v_, Aug 16 2006

%E a(9)-a(10) from _Robert G. Wilson v_, Sep 03 2012