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A063084
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a(n) = pi(n-1)*n - pi(n)*(n-1), where pi() = A000720().
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1
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0, -1, -1, 2, -2, 3, -3, 4, 4, 4, -6, 5, -7, 6, 6, 6, -10, 7, -11, 8, 8, 8, -14, 9, 9, 9, 9, 9, -19, 10, -20, 11, 11, 11, 11, 11, -25, 12, 12, 12, -28, 13, -29, 14, 14, 14, -32, 15, 15, 15, 15, 15, -37, 16, 16, 16, 16, 16, -42, 17, -43, 18, 18, 18, 18, 18, -48, 19, 19, 19, -51, 20, -52, 21, 21, 21, 21, 21, -57, 22, 22, 22, -60, 23, 23
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OFFSET
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1,4
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COMMENTS
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To define as positive sequence let C(n)= A062298; f(a) = pi(a) if a is nonprime, f(a)= C(a) if a is prime. - Daniel Tisdale, Nov 07 2008
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REFERENCES
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G. A. Kudrevatow, (1970): Exercises in Number Theory. Problem 488; page 56; Prosveshenie, Moscow [in Russian].
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LINKS
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EXAMPLE
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The function is positive for composite and negative for prime numbers. It is zero at n=1.
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PROG
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(PARI) a(n)={if(n>1, primepi(n-1)*n - primepi(n)*(n-1), 0)} \\ Harry J. Smith, Aug 17 2009
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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