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A330275 Integers n such that lcm(1, ..., n) > exp(n). 1

%I #24 Sep 08 2022 08:46:24

%S 19,31,32,43,47,49,53,61,73,74,75,79,83,84,89,103,107,109,110,111,112,

%T 113,114,115,116,117,131,139,140,141,151,169,173,174,179,181,182,183,

%U 184,185,193,194,195,197,198,199,200,201,202,203,204,205,206,211,233

%N Integers n such that lcm(1, ..., n) > exp(n).

%C It is well known that lcm(1, ..., n) is approximately exp(n). For most numbers < 100 it is less than exp(n).

%H Robert Israel, <a href="/A330275/b330275.txt">Table of n, a(n) for n = 1..10000</a>

%H J. Barkley Rosser and Lowell Schoenfeld, <a href="http://doi.org/10.1215/ijm/1255631807">Approximate formulas for some functions of prime numbers</a>, Illinois Journal of Mathematics, Vol. 6, No. 1 (1962), pp. 64-94.

%p select(n -> is(ilcm($1..n) > exp(n)), [$1..300]); # _Robert Israel_, Dec 08 2019

%t Select[Range[233], LCM @@ Range[#] > Exp[#] &] (* _Amiram Eldar_, Dec 08 2019 *)

%o (PARI) c=1; for (n=1, 233, c=lcm(c,n); if (c>exp(n), print1 (n", "))) \\ _Rémy Sigrist_, Dec 08 2019

%o (Magma) [k:k in [1..250]|Lcm([1..k]) gt Exp(k)]; // _Marius A. Burtea_, Dec 16 2019

%Y Cf. A003418.

%K nonn

%O 1,1

%A _Wendy Appleby_, Dec 08 2019

%E More terms from _Rémy Sigrist_, Dec 08 2019

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Last modified March 29 08:13 EDT 2024. Contains 371265 sequences. (Running on oeis4.)