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A186749
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a(n) = phi(n - phi(n) + 3).
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2
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2, 2, 2, 4, 2, 6, 2, 6, 2, 6, 2, 10, 2, 10, 4, 10, 2, 8, 2, 8, 4, 8, 2, 18, 4, 16, 4, 18, 2, 20, 2, 18, 8, 12, 6, 18, 2, 22, 6, 18, 2, 20, 2, 18, 8, 18, 2, 24, 4, 20, 10, 30, 2, 24, 6, 24, 8, 20, 2, 46, 2, 24, 8, 24, 8, 42, 2, 24, 12, 42, 2, 32, 2, 40, 18, 42
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OFFSET
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1,1
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COMMENTS
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This is the Euler Phi function of 3 more than the Cototient of n.
If n is noncomposite, a(n) = 2. Proof: For n = 1, phi(1 - phi(1) + 3) = phi(1-1+3) = phi(3) = 2. For n = p, phi(p - phi(p) + 3) = phi(p - (p-1) + 3) = phi(4) = 2.
If n is the product of twin primes, a(n) is the arithmetic mean of the prime factors. Equivalently, when n is the product of twin primes, a(n) +- 1 represents the largest and the smallest prime factors of n respectively.
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LINKS
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FORMULA
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EXAMPLE
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a(15) = 4, Since phi(15 - phi(15) + 3) = 4. Note that 15 is the product of twin primes and that a(15) = 4 is the arithmetic mean of the prime factors of 15: (3+5)/2 = 4.
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MAPLE
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with(numtheory); seq( phi(k - phi(k) + 3), k=1..70);
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MATHEMATICA
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Table[EulerPhi[n - EulerPhi[n] + 3], {n, 100}]
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PROG
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(Magma) [EulerPhi(n-EulerPhi(n)+3): n in [1..100]]; // Vincenzo Librandi, Dec 08 2015
(GAP) List([1..70], n->Phi(n-Phi(n)+3)); # Muniru A Asiru, Mar 04 2018
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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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