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A101993
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Indices n for which the numerator of Sum( (-1)^i/(i * phi(i)) ) 2<=i<=n is a prime number.
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0
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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EXAMPLE
| a(1) = 4 because numerator of Sum((-1)^i/(i * phi(i))) is 11 and 11 is a prime number.
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MATHEMATICA
| 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 (stefan.steinerberger(AT)gmail.com), Apr 02 2006
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CROSSREFS
| Cf. Euler's totient function phi(n) : A000010 The sequence of the numerator of the sum : A101992.
Sequence in context: A080746 A069909 A189715 * A002481 A183870 A186497
Adjacent sequences: A101990 A101991 A101992 * A101994 A101995 A101996
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KEYWORD
| more,nonn
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AUTHOR
| Orges Leka (oleka(AT)students.uni-mainz.de), Dec 23 2004
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EXTENSIONS
| More terms from Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Apr 02 2006
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