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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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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
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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. 1 and 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 = Product_{k>0} ((1-A002145(k)^(-2))^(-1/2)).
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MATHEMATICA
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With[{s = {1}~Join~Select[Range@ 80, AllTrue[FactorInteger[#][[All, 1]], Mod[#, 4] == 3 &] &]}, Table[LengthWhile[s, # <= n &], {n, Max@ s}]] (* Michael De Vlieger, Jul 30 2017 *)
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PROG
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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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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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