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A071903 Number of x less than or equal to n and divisible only by primes congruent to 3 mod 4 (i.e., in A004614). 2
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; refs; listen; history; text; internal format)
OFFSET

0,3

REFERENCES

Landau, "Handbuch der Lehre von der Verteilung der Primzahlen", vol. 2, Teubner, Leipzig; third edition: Chelsea, New York (1974), pp. 641-669.

LINKS

Michael De Vlieger, Table of n, a(n) for n = 0..10000

E. Landau, Handbuch der Lehre von der Verteilung der Primzahlen, vol. 2, Leipzig, Berlin, B. G. Teubner, 1909.

E. Landau, Handbuch der Lehre von der Verteilung der Primzahlen, vol. 1 and vol. 2, Leipzig, Berlin, B. G. Teubner, 1909.

FORMULA

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)).

MATHEMATICA

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 *)

PROG

(PARI) for(n=1, 100, print1(sum(i=1, n, if(sumdiv(i, d, isprime(d)*(d-3)%4), 0, 1)), ", "))

CROSSREFS

Cf. A002145, A004614.

Sequence in context: A225643 A116563 A076695 * A091372 A185322 A324918

Adjacent sequences:  A071900 A071901 A071902 * A071904 A071905 A071906

KEYWORD

easy,nonn

AUTHOR

Benoit Cloitre, Jun 12 2002

STATUS

approved

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Last modified November 18 22:50 EST 2019. Contains 329305 sequences. (Running on oeis4.)