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A072114
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Number of 3-almost primes (A014612) <= n.
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4
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0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 4, 4, 4, 4, 4, 4, 4, 5, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 9, 10, 10, 10, 10, 10, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 14, 14, 15, 15, 16, 16, 16, 16, 16, 17, 18, 18, 19, 19, 19, 19, 19, 19, 19
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,13
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COMMENTS
| Number of k <= n such that bigomega(k) = 3.
Let A be a positive integer then card{ x <= n : bigomega(x) = A } ~ (n/Log(n))*Log(Log(n))^(A-1)/(A-1)!. For which n, card{ x <= n : bigomega(x) = 3 } >= card{ x <= n : bigomega(x) = 2 } ?
n=15530 is the first number for which are are more 3-almost primes than 2-almost primes. See A125149.
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REFERENCES
| E. Landau, Handbuch der Lehre von der Verteilung der Primzahlen, vol. 1, Teubner, Leipzig; third edition : Chelsea, New York (1974).
G. Tenenbaum, Introduction \`a la th\'eorie analytique et probabiliste des nombres, p. 203, Publications de l'Institut Cartan, 1990.
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FORMULA
| a(n) = card{ x <= n : bigomega(x) = 3 }, asymptotically : a(n) ~ (n/log(n))*log(log(n))^2/2 [Landau, p. 211]
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PROG
| (PARI) for(n=1, 100, print1(sum(i=1, n, if(bigomega(i)-3, 0, 1)), ", "))
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CROSSREFS
| Cf. A014612, A109251, A001358, A072000.
Sequence in context: A092670 A120450 A127238 * A090621 A173711 A029378
Adjacent sequences: A072111 A072112 A072113 * A072115 A072116 A072117
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KEYWORD
| easy,nonn
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AUTHOR
| Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 19 2002
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