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Search: id:A071903
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| A071903 |
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Number of x less than or equal to n and divisible only by primes congruent to 3 mod 4 (i.e. in A004614). |
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+0
2
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| 1, 1, 2, 2, 2, 2, 3, 3, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 13, 13, 14, 14, 14, 14, 14, 14, 14, 14, 15, 15, 16, 16, 16, 16, 17, 17, 17, 17, 18, 18, 19, 19, 20, 20, 20, 20, 20, 20, 21, 21, 22
(list; graph; listen)
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OFFSET
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0,3
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REFERENCES
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Landau, "Handbuch der Lehre von der Verteilung der Primzahlen", vol. 2, Teubner, Leipzig; third edition : Chelsea, New York (1974), pp. 641-669
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LINKS
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E. Landau, Handbuch der Lehre von der Verteilung der Primzahlen, vol. 2, Leipzig, Berlin, B. G. Teubner, 1909.
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FORMULA
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a(n) = Card{ k | A004614(k) <= n }, asymptotically : a(n) ~ sqrt(2)*A*n/(Pi*sqrt(Log(n))) where A = Prod(k>0, (1-A002145(k)^(-2))^(-1/2))
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PROGRAM
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(PARI) for(n=1, 100, print1(sum(i=1, n, if(sumdiv(i, d, isprime(d)*(d-3)%4), 0, 1)), ", "))
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CROSSREFS
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Cf. A004614, A002145.
Sequence in context: A008668 A116563 A076695 this_sequence A091372 A068980 A053266
Adjacent sequences: A071900 A071901 A071902 this_sequence A071904 A071905 A071906
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KEYWORD
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easy,nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 12 2002
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