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

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..100

Example

a(1) = 4 because numerator of Sum_{i=2..4} ((-1)^i/(i * phi(i))) is 11 and 11 is a prime number.

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 *)

Prog

(PARI) isok(n) = isprime(numerator(sum(k=2, n, (-1)^k/(k*eulerphi(k))))); \\ Michel Marcus, Aug 27 2015

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).

Sequence in context: A069909 A189715 A393587 * A370267 A002481 A370268

Adjacent sequences: A101990 A101991 A101992 * A101994 A101995 A101996

Keyword

nonn

Author

Orges Leka, Dec 23 2004

Extensions

More terms from Stefan Steinerberger, Apr 02 2006

More terms from Amiram Eldar, Jul 13 2019

Status

approved