login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A284411 Least prime p such that more than half of all integers are divisible by n distinct primes not greater than p. 7

%I #33 May 06 2021 08:11:44

%S 3,37,42719,5737850066077

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

%C 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.

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

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

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

%H Gérald Tenenbaum, <a href="https://hal.archives-ouvertes.fr/hal-01281530/document">Some of Erdos' unconventional problems in number theory, thirty-four years later.</a> Erdos Centennial, Janos Bolyai Math. Soc., 2013, 651-681. HAL Id: hal-01281530

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

%e 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.

%Y Cf. A002110, A096294, A194156, A281889.

%K nonn,more,hard

%O 1,1

%A _Peter Munn_, Mar 26 2017

%E Definition edited by _N. J. A. Sloane_, Apr 01 2017

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 04:13 EDT 2024. Contains 371235 sequences. (Running on oeis4.)