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A284411 Least prime p such that more than half of all integers are divisible by n distinct primes not greater than p. 2
3, 37, 42719, 5737850066077 (list; graph; refs; listen; history; text; internal format)
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, 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, 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

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Last modified May 19 02:45 EDT 2019. Contains 323377 sequences. (Running on oeis4.)