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A048866
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Difference between number of nonprimes and primes in reduced residue system of n.
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3
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1, 1, 0, 0, 0, 0, 0, -2, 0, 0, 2, -2, 2, -2, 0, -2, 4, -4, 4, -4, 0, -2, 6, -6, 4, -2, 2, -2, 10, -6, 10, -4, 2, -2, 6, -6, 14, -2, 4, -4, 16, -8, 16, -4, 0, -2, 18, -10, 14, -6, 6, -2, 22, -10, 12, -4, 8, 0, 26, -12, 26, -2, 4, -2, 16, -10, 30, -2, 10, -8, 32, -12, 32, -2, 2, -2
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OFFSET
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1,8
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LINKS
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FORMULA
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EXAMPLE
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n = 31: Phi(31) = 30 from which 10 is prime and 20 is not: a(31) = 20-10 = 10;
n = 20: Phi(20) = 8 from which 6 are primes and 2 are not: a(20) = 2-6 = -4;
n = 15: reduced residue system = {1,2,7,4,8,11,13,14}, primes = {2,7,11,13,}, nonprimes = {2,4,8,14}, thus a(15) = 4-4 = 0.
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MATHEMATICA
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Table[EulerPhi[n] - 2*PrimePi[n] + 2*PrimeNu[n] , {n, 1, 50}] (* G. C. Greubel, May 12 2017 *)
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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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