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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. 6
 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 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, 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

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Last modified May 26 13:49 EDT 2020. Contains 334626 sequences. (Running on oeis4.)