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A038625
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a(n) is smallest number m such that m = n*pi(m), where pi(k) = number of primes <= k (A000720).
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22
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2, 27, 96, 330, 1008, 3059, 8408, 23526, 64540, 175197, 480852, 1304498, 3523884, 9557955, 25874752, 70115412, 189961182, 514272411, 1394193580, 3779849598, 10246935644, 27788566029, 75370121160, 204475052375, 554805820452, 1505578023621, 4086199301996, 11091501630949
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OFFSET
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2,1
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COMMENTS
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Golomb shows that solutions exist for each n>1.
Equivalently, for n > 1, least m such that m >= n*pi(m). - Eric M. Schmidt, Aug 05 2014
The values a(26),...,a(50) were calculated with the Eratosthenes sieve making use of strong bounds for pi(x), which follow from partial knowledge of the Riemann hypothesis, and the analytic method for calculating initial values of pi(x). - Jan Büthe, Jan 16 2015
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LINKS
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FORMULA
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EXAMPLE
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pi(3059) = 437 and 3059/437 = 7, so a(7)=3059.
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MAPLE
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with(numtheory); f:=proc(n) local i; for i from 2 to 10000 do if i mod pi(i) = 0 and i/pi(i) = n then RETURN(i); fi; od: RETURN(-1); end; # N. J. A. Sloane, Sep 01 2008
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MATHEMATICA
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t = {}; k = 2; Do[While[n*PrimePi[k] != k, k++]; AppendTo[t, k], {n, 2, 15}]; t (* Jayanta Basu, Jul 10 2013 *)
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PROG
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(PARI)
a(n)=my(k=1); while(k!=n*primepi(k), k++); k;
for (n=2, 20, print1(a(n), ", ")); \\ Derek Orr, Aug 13 2014
(Python)
from math import exp
from sympy import primepi
def a(n):
m = 2 if n == 2 else int(exp(n)) # pi(m) > m/log(m) for m >= 17
while m != n*primepi(m): m += 1
return m
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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24 terms added and entry a(26) corrected by Jan Büthe, Jan 07 2015
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STATUS
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approved
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