A271568 Squarefree semiprimes n such that phi(n) - 1 is prime.

10, 14, 15, 21, 26, 33, 35, 38, 39, 51, 62, 65, 69, 77, 86, 91, 93, 95, 111, 122, 123, 129, 133, 146, 159, 161, 201, 203, 206, 209, 213, 215, 217, 218, 221, 249, 278, 287, 291, 299, 301, 302, 303, 305, 321, 335, 339, 362, 371, 381, 386, 395, 398, 403

Offset

1,1

Comments

Equals (A001358 intersection A078892) - A001248.

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Example

15 is in the sequence, because 15 = 3*5 is a semiprime with omega(15) = 2 and phi(15) - 1 = 2*4 - 1 = 7 is a prime.
21 is in the sequence, because 21 = 3*7 is a semiprime with omega(21) = 2 and phi(21) - 1 = 2*6 - 1 = 11 is a prime.

Maple

with(numtheory):
is_A271568 := n -> issqrfree(n) and bigomega(n) = 2 and isprime(phi(n)-1):
select(is_A271568, [$1..403]); # Peter Luschny, Jul 21 2016

Mathematica

A271568Q = SquareFreeQ[#] && PrimeNu[#] == 2 && PrimeQ[EulerPhi[#] - 1] &; Select[Range[500], A271568Q] (* JungHwan Min, Jul 29 2016 *)

Prog

(PARI) is_a001358(n) = bigomega(n)==2
is_a005117(n) = issquarefree(n)
is_a078892(n) = ispseudoprime(eulerphi(n)-1)
is(n) = is_a001358(n) && is_a005117(n) && is_a078892(n) \\ Felix Fröhlich, Jul 21 2016
(PARI) is(n)=my(f=factor(n)); f[, 2]==[1, 1]~ && isprime((f[1, 1]-1)*(f[2, 1]-1)-1) \\ Charles R Greathouse IV, Jul 21 2016
(PARI) list(lim)=my(v=List()); forprime(p=2, sqrt(lim), forprime(q=p+1, lim\p, if(isprime((p-1)*(q-1)-1), listput(v, p*q)))); Set(v) \\ Charles R Greathouse IV, Aug 29 2016
(Magma) [n: n in [1..500] |(EulerPhi(n)+DivisorSigma(1, n)) eq 2*(n+1) and IsPrime(EulerPhi(n)-1)]; // Vincenzo Librandi, Jul 29 2016

Crossrefs

Cf. A001358, A078892, A001248.

Sequence in context: A307507 A171156 A235690 * A229271 A088711 A154774

Adjacent sequences: A271565 A271566 A271567 * A271569 A271570 A271571

Keyword

nonn

Author

Debapriyay Mukhopadhyay, Jul 13 2016

Extensions

New name from Charles R Greathouse IV, Jul 29 2016

Status

approved