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

19, 31, 32, 43, 47, 49, 53, 61, 73, 74, 75, 79, 83, 84, 89, 103, 107, 109, 110, 111, 112, 113, 114, 115, 116, 117, 131, 139, 140, 141, 151, 169, 173, 174, 179, 181, 182, 183, 184, 185, 193, 194, 195, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 211, 233

Offset: 1

Author

Wendy Appleby, Dec 08 2019

Keywords

• nonn

Comments

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

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• J. Barkley Rosser and Lowell Schoenfeld, Approximate formulas for some functions of prime numbers, Illinois Journal of Mathematics, Vol. 6, No. 1 (1962), pp. 64-94.

Crossrefs

Cf. A003418.

Programs

Magma

[k:k in [1..250]|Lcm([1..k]) gt Exp(k)]; // Marius A. Burtea, Dec 16 2019

Maple

select(n -> is(ilcm($1..n) > exp(n)), [$1..300]); # Robert Israel, Dec 08 2019

Mathematica

Select[Range[233], LCM @@ Range[#] > Exp[#] &] (* Amiram Eldar, Dec 08 2019 *)

PARI

c=1; for (n=1, 233, c=lcm(c,n); if (c>exp(n), print1 (n", "))) \\ Rémy Sigrist, Dec 08 2019

Extensions

More terms from Rémy Sigrist, Dec 08 2019