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A036234
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Number of primes <= n, if 1 is counted as a prime.
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28
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1, 2, 3, 3, 4, 4, 5, 5, 5, 5, 6, 6, 7, 7, 7, 7, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 11, 11, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 14, 14, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 18, 18, 19, 19, 19, 19, 19, 19, 20, 20, 20, 20
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OFFSET
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1,2
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COMMENTS
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This sequence is the largest nondecreasing sequence a(n) such that a(Prime(n)-1) = n. - Tanya Khovanova, Jun 20 2007
Let G(n) be the graph whose vertices represent integers 1 through n, and where vertices a and b are adjacent iff gcd(a,b)>1. Then a(n) is the independence number of G(n). - Aaron Dunigan AtLee, May 23 2009
It appears that a(n) is the minimal index i for which binomial(k*prime(i), prime(i)) mod prime(i) = k. For example, binomial(11*prime(n), prime(n)) mod prime(n) produces the sequence 1,2,1,4,0,11,11,11,11 and a(11)=6. It also appears that binomial(k*prime(a(n)-1), prime(a(n)-1)) mod prime(a(n)-1) = 0 iff k is prime. - Gary Detlefs, Aug 05 2013
a(n) is the number of noncomposite numbers <= n. The noncomposite number are in A008578. - Omar E. Pol, Aug 31 2013
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LINKS
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FORMULA
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MAPLE
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if n = 1 then
1;
else
1+numtheory[pi](n) ;
end if;
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MATHEMATICA
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PROG
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(Haskell)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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