

A330275


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


1



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
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OFFSET

1,1


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. 6494.


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 *)


PROG

(PARI) c=1; for (n=1, 233, c=lcm(c, n); if (c>exp(n), print1 (n", "))) \\ Rémy Sigrist, Dec 08 2019
(MAGMA) [k:k in [1..250]Lcm([1..k]) gt Exp(k)]; // Marius A. Burtea, Dec 16 2019


CROSSREFS

Cf. A003418.
Sequence in context: A298763 A309962 A316678 * A038672 A250216 A125148
Adjacent sequences: A330272 A330273 A330274 * A330276 A330277 A330278


KEYWORD

nonn


AUTHOR

Wendy Appleby, Dec 08 2019


EXTENSIONS

More terms from Rémy Sigrist, Dec 08 2019


STATUS

approved



