A284411 Least prime p such that more than half of all integers are divisible by n distinct primes not greater than p.

3, 37, 42719, 5737850066077

Offset

1,1

Comments

The proportion of all integers that satisfy the divisibility criterion for p=prime(m) is determined using the proportion that satisfy it over any interval of primorial(m)=A002110(m) integers.

a(4) is from De Koninck, 2009; calculation credited to D Grégoire.

References

J.-M. De Koninck, Those Fascinating Numbers, American Mathematical Society, 2009.

Links

Table of n, a(n) for n=1..4.

J. de Koninck and G. Tenenbaum, Sur la loi de répartition du k-ième facteur premier d'un entier, Mathematical Proceedings of the Cambridge Philosophical Society, 133(2), 191-204. doi:10.1017/S0305004102005972

Gérald Tenenbaum, Some of Erdos' unconventional problems in number theory, thirty-four years later. Erdos Centennial, Janos Bolyai Math. Soc., 2013, 651-681. HAL Id: hal-01281530

Formula

a(n) is least p=prime(m) such that 2*Sum_{k=0..n-1} A096294(m,k) < A002110(m).

Example

Exactly half of the integers are divisible by 2, so a(1)>2. Two-thirds of all integers are divisible by 2 or 3, so a(1) = 3.

Crossrefs

Cf. A002110, A096294, A194156, A281889.

Sequence in context: A172029 A120480 A088098 * A176245 A122787 A241895

Adjacent sequences: A284408 A284409 A284410 * A284412 A284413 A284414

Keyword

nonn,more,hard

Author

Peter Munn, Mar 26 2017

Extensions

Definition edited by N. J. A. Sloane, Apr 01 2017

Status

approved