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A244111 Primes p such that p + phi(p) + mu(phi(p)) is also prime. 1
19, 37, 97, 157, 199, 229, 271, 307, 337, 379, 577, 601, 661, 727, 811, 829, 877, 937, 997, 1009, 1069, 1171, 1237, 1279, 1297, 1429, 1459, 1531, 1609, 1657, 2029, 2089, 2137, 2179, 2221, 2281, 2467, 2539, 2551, 2557, 2617, 2719, 2791, 2851, 3037, 3061, 3109 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

For these terms, mu(phi(p)) must be zero.

For prime p, phi(p) = p-1, so terms are primes p such that 2p-1 is also prime (A005382) and p-1 is not squarefree. - Jens Kruse Andersen, Jul 19 2014

LINKS

Jens Kruse Andersen, Table of n, a(n) for n = 1..10000

EXAMPLE

a(1)=19 as 19+18+0 is prime.

a(2)=37 as 37+36+0 is prime.

a(3)=97 as 97+96+0 is prime.

MAPLE

with(numtheory): A244111:=n->`if`(isprime(n+phi(n)+mobius(phi(n))) and isprime(n), n, NULL); seq(A244111(n), n=1..5000); # Wesley Ivan Hurt, Jul 19 2014

MATHEMATICA

apQ[n_]:=Module[{p=EulerPhi[n]}, PrimeQ[n+p+MoebiusMu[p]]]; Select[Prime[ Range[500]], apQ] (* Harvey P. Dale, Jun 13 2015 *)

PROG

(PARI) isok(n) = isprime(n) && isprime(n + eulerphi(n) + moebius(eulerphi(n))); \\ Michel Marcus, Jun 21 2014

CROSSREFS

Cf. A000010, A005382, A008683.

Sequence in context: A257074 A299930 A053685 * A136063 A242979 A244931

Adjacent sequences:  A244108 A244109 A244110 * A244112 A244113 A244114

KEYWORD

nonn

AUTHOR

Torlach Rush, Jun 20 2014

EXTENSIONS

More terms from Michel Marcus, Jun 21 2014

STATUS

approved

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Last modified November 28 06:42 EST 2021. Contains 349401 sequences. (Running on oeis4.)