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A101993
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Indices k for which the numerator of Sum_{i=2..k} ( (-1)^i/(i * phi(i)) ) is a prime number.
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1
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4, 6, 7, 9, 10, 13, 16, 21, 27, 35, 39, 41, 45, 48, 52, 76, 84, 94, 119, 150, 165, 190, 251, 260, 264, 306, 416, 428, 488, 513, 521, 523, 553, 615, 622, 640, 711, 714, 765, 797, 807, 888, 967, 1146, 1292, 1555, 1602, 1750, 1822, 1859, 1868, 1950, 2009, 2059
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OFFSET
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1,1
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LINKS
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EXAMPLE
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a(1) = 4 because numerator of Sum_{i=2..4} ((-1)^i/(i * phi(i))) is 11 and 11 is a prime number.
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MATHEMATICA
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(* Defining the sum: *) f[n_Integer] /; n >= 2 := Sum[(-1)^(i)/(i EulerPhi[i]), {i, 2, n}] (* Generating the sequence: *) PhiPrimes[n_Integer] /; n >= 2 := Flatten[Table[If[PrimeQ[Numerator[f[i]]], i, {}], {i, 2, n}]] (* Checking if a given n is a phi-prime: *) PhiPrimeQ[n_Integer] /; n >= 2 := If[PrimeQ[ Numerator[f[n]]], Numerator[f[n]], "not a phi-prime"]
Select[Range[2, 1300], PrimeQ[Numerator[Sum[(-1)^i/(i*EulerPhi[i]), {i, 2, #}]]] &] (* Stefan Steinerberger, Apr 02 2006 *)
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PROG
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(PARI) isok(n) = isprime(numerator(sum(k=2, n, (-1)^k/(k*eulerphi(k))))); \\ Michel Marcus, Aug 27 2015
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CROSSREFS
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Cf. A000010 (Euler's totient function phi(n)).
Cf. A101992 (the sequence of the numerator of the sum described in the name of the current sequence).
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KEYWORD
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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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