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

Author

Orges Leka (oleka(AT)students.uni-mainz.de), Dec 23 2004

Keywords

• nonn

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

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).

Programs

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