A101993 Indices k for which the numerator of Sum_{i=2..k} ( (-1)^i/(i * phi(i)) ) is a prime number.
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
Offset: 1
Keywords
Examples
a(1) = 4 because numerator of Sum_{i=2..4} ((-1)^i/(i * phi(i))) is 11 and 11 is a prime number.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..100
Crossrefs
Programs
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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, Apr 02 2006 *) -
PARI
isok(n) = isprime(numerator(sum(k=2, n, (-1)^k/(k*eulerphi(k))))); \\ Michel Marcus, Aug 27 2015
Extensions
More terms from Stefan Steinerberger, Apr 02 2006
More terms from Amiram Eldar, Jul 13 2019