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A210500
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Number of even solutions to phi(k) = prime(n) - 1.
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4
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1, 2, 3, 2, 1, 4, 5, 2, 1, 1, 1, 5, 6, 2, 1, 1, 1, 5, 1, 1, 11, 1, 1, 4, 13, 2, 1, 1, 5, 4, 1, 1, 1, 1, 1, 1, 4, 2, 1, 1, 1, 5, 1, 17, 1, 1, 1, 1, 1, 1, 4, 1, 21, 1, 9, 1, 1, 1, 5, 5, 1, 1, 1, 1, 10, 1, 1, 13, 1, 3, 9, 1, 1, 1, 1, 1, 1, 7, 9, 4, 1, 7, 1, 23, 1, 1, 9
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OFFSET
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1,2
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COMMENTS
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REFERENCES
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Alexander S. Karpenko, Lukasiewicz's Logics and Prime Numbers, Luniver Press, Beckington, 2006, pp. 52-56.
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LINKS
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FORMULA
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EXAMPLE
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The set {k: phi(k) = 12} is {13, 21, 26, 28, 36, 42}. Thus, if phi(k) = prime(6) - 1, the equation has exactly four even solutions. Hence, a(6) = 4.
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MATHEMATICA
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r = 87; lst1 = Table[EulerPhi[n], {n, (Prime[r] - 1)^2 + 2}]; lst2 = {}; Do[p = Prime[n]; AppendTo[lst2, Length@Select[Flatten@Position[Take[lst1, {p - 1, (p - 1)^2 + 2}], Prime[n] - 1], OddQ]], {n, r}]; lst2
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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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