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A101992
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Numerator of Sum_{i=2..n} ((-1)^i/(i phi(i))).
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2
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1, 1, 11, 49, 59, 131, 559, 14533, 15289, 33031, 34417, 441877, 452173, 2224829, 9034451, 152504587, 155227307, 2932982513, 2967901397, 2945730677, 2971126229, 6189267977, 6250111487, 155668689479, 156604743479, 1404034379311, 1411857116311, 5835711932717
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OFFSET
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2,3
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COMMENTS
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I conjecture that there exists a limit for Sum_{i>=2} ((-1)^i/(i*phi(i)) which is ca. 0.558.
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LINKS
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FORMULA
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a(n) = numerator( Sum_{i=2..n} ((-1)^i/(i*phi(i))) ).
Sum_{i>=2} ((-1)^i/(i phi(i))) = 1 - (1/5) * A065484 = 0.5592286807... . - Amiram Eldar, Nov 21 2022
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EXAMPLE
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a(3) = 11 because Sum_{i=2..3} ( (-1)^i/(i*phi(i)) = 11/24, so the numerator of 11/24 is 11.
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MATHEMATICA
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(* Generating the sum : *) f[n_Integer]/; n >= 2 := Sum[(-1)^i/(i*EulerPhi[i]), {i, 2, n}]; (* Getting the numerator: *) a[n_Integer]/; n >=2 := Numerator[f[n]]; (* Generating the sequence : *) Table[a[n], {n, 2, 20}]
Accumulate[Table[(-1)^n/(n EulerPhi[n]), {n, 2, 30}]]//Numerator (* Harvey P. Dale, Mar 19 2023 *)
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CROSSREFS
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KEYWORD
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frac,nonn
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AUTHOR
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Orges Leka (oleka(AT)students.uni-mainz.de), Dec 23 2004
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EXTENSIONS
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STATUS
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approved
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