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A097454
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a(n) = (number of nonprimes <= n) - (number of primes <= n).
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4
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1, 0, -1, 0, -1, 0, -1, 0, 1, 2, 1, 2, 1, 2, 3, 4, 3, 4, 3, 4, 5, 6, 5, 6, 7, 8, 9, 10, 9, 10, 9, 10, 11, 12, 13, 14, 13, 14, 15, 16, 15, 16, 15, 16, 17, 18, 17, 18, 19, 20, 21, 22, 21, 22, 23, 24, 25, 26, 25, 26, 25, 26, 27, 28, 29, 30, 29, 30, 31, 32, 31, 32, 31, 32, 33, 34, 35, 36, 35, 36, 37, 38, 37, 38, 39, 40, 41, 42, 41, 42, 43, 44, 45
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OFFSET
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1,10
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LINKS
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FORMULA
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EXAMPLE
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a(7) = -1 because there are 3 nonprimes <= 7 (1,4 and 6) and 4 primes <= 7 (2,3,5 and 7).
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MAPLE
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with(numtheory): seq(n-2*pi(n), n=1..93); # Emeric Deutsch, Apr 01 2006
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MATHEMATICA
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Accumulate[ -1 + 2 * Boole /@ Not /@ PrimeQ @ Range @ 100] (* Federico Provvedi, Oct 06 2013 *)
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PROG
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(PARI)
compsmprimes(n) = { for(x=1, n, y=composites(x) - pi(x); print1(y", ") ) }
\\ The number of composite numbers less than or equal to n
composites(n) = { my(c, x); c=0; for(x=1, n, if(!isprime(x), c++); ); return(c) }
\\ pi(x) prime count function
pi(n) = { my(c, x); c=0; forprime(x=1, n, c++); return(c) }
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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STATUS
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approved
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